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THE

FORCES OF NATURE

A POPULAR INTRODUCTION TO THE STUDY
OF PHYSICAL PHENOMENA.

AMEDEE GUILLEMIN.

TRANSLATED FROM THE FRENCH BY

MRS. NORMAN LOCKYER;

AND EDITED, WITH ADDITIONS AND NOTES, BY

J. NORMAN LOCKYER, F.R.S.

TWO COLOURED PLATES, A PHOTOGRAPH, AND FOUR HUNDRED AND FIFTY- SIX

WOODCUTS.

THIRD EDITION.

MACMILLAN AND CO.

1877.

LONDON :

R CI-AY, SONS, AND TAYLOR,
BREAD STREET HII.L.

PREFACE.

"HI ROM time immemorial the mind of man has felt a strong
desire to fathom the laws which govern the various
phenomena of Nature, and to understand her in her most
secret work — in short, to make itself master of her forces, in
order to render them as useful to material as to intellectual
and moral life ; such is the noble undertaking to which the
greatest minds have devoted themselves. For too long did
man wander in this eager and often dangerous pursuit of
truth : beginning with fanciful interpretations in his infancy,
he by degrees substituted hypothesis for fable ; and then, at
length, understanding the true method, that of experimental
observation, he has been able, after innumerable efforts, to
give in imperishable formulae, the most general idea of the
principal phenomena of the physical world.

In order thus to place itself in communion with Nature,
our intelligence draws from two springs, both bright and
pure, arid equally fruitful — Art and Science : but it is by
different, we may say even by opposite, methods that these
springs at which man may satisfy his thirst for the ideals,
which constitute his nobleness and greatness, the love of the
beautiful, truth and justice, have been reached. The artist
abstains from dulling the brilliancy of his impressions by a

PREFACE.

cold analysis ; the man of science, on the contrary, in pre-
sence of Nature, endeavours only to strip off the magnificent
and poetical surroundings, to dissect it, so to speak, in order
to dive into all the hidden secrets ; but his enjoyment is not
less than that of the artist, when he has succeeded in recon-
structing, in its intelligible whole, this world of pheno-
mena of which his power of abstraction has enabled him to
investigate the laws.

We must not seek then in the study of physical pheno-
mena, from a purely scientific point of view, the fascination
of poetical or picturesque description ; on the other hand,
such a study is eminently fit to satisfy that invincible
tendency of our minds, which urges us on to understand
the reason of things — that fatality which dominates us, but
which it is possible for us to make use of to the free and
legitimate satisfaction of our faculties.

Gravity, Sound. Heat, Electricity, and Light are the
divisions under which are arranged the phenomena the
description of which forms the object of this work. The
programme has not been confined to a simple explanation of
the facts : but an attempt has been made to grasp their
relative bearings, or, in other words, their laws ; a slightly
difficult task, perhaps, when we cannot use the clear and
simple language of mathematics. It may be added that the
present work has been carried out in the same spirit as the
astronomical one, " The Heavens ; " which is sufficient to
show that there has been neither the thought nor the
intention to compile a Treatise on Physics ; I have been
content to smooth the way for those who desire to extend
their studies, and likewise to present to general readers a
sufficiently exact and just idea of this branch of science.

PREFACE. vii

In this attempt at a description of physical phenomena T
have drawn from numerous sources, too long to enumerate,
science having developed so much during the last two cen-
turies ; but I should fail in a simple act of justice, if I
did not express my gratitude to one of our most learned
physicists, M. le Eoux, who was kind enough to read over
most of the proofs of the work, and whose judicious advice
has been of so much use to me.

I must acknowledge the valuable aid of the artists,
especially of MM. Bonnafoux and Laplante, Digeon and
Rapine, who have designed or engraved the coloured plates
and woodcuts.

AMEDEE GUILLEMIN.

CONTENTS.

BOOK I.

G R A V I T 7.
CHAPTER I.

PHENOMENA OF GRAVITY ON THE SURFACE OF THE EARTH.

Manifestation of weight by motion : fall of bodies, flowing of liquids, ascent of
gas — Pressure of bodies in equilibrium ; stability of the various solid, liquid,
and gaseous strata which constitute the terrestrial globe — Crumbling away of
mountains ; fall of avalanches and of blocks of ice in the polar regions— Air
and sea currents Page 3

CHAPTER II.

WEIGHT AND UNIVERSAL GRAVITATION.

Common tendency of heavy bodies to fall towards the centre of the earth — Weight
is a particular case of the force of universal gravitation — All the particles
of the globe act on a falling stone as if they were all situated in the
centre of the earth — The force of gravity acts beyond the atmosphere even
in the celestial spaces : the sun, planets, stars— all bodies — gravitate towards
each other Page 10

CHAPTER III.

LAWS OF ATTRACTION. — FALLING BODIES.

First experiments of Galileo on falling bodies— Equal velocity of bodies falling
in vacua — Vertical direction of gravity — Deviation from the vertical due
to the rotation of the earth — Galileo's inclined plane ; Attwood's machine ;
Morin's machine ; laws of falling bodies — Influence of the resistance of the
air on the velocity of bodies falling through the atmosphere ; experiments of
Desagulier Page 16

CONTENTS.

CHAPTER IV.

LAWS OF GRAVITY. — THE PENDULUM.

The Pendulum — Galileo's observations — Definition of the simple pendulum— Iso-
chronism of oscillations of small amplitude — Relation between the time of
the oscillations and the length of the pendulum — Variations of the force of
gravity in different latitudes — Borda's pendulum — Lengths of the pendulums
which beat seconds in London, at the equator, and at the poles — Calculation
of the oblateness of the earth — Experiments proving that the density of the
earth increases from the surface to the centre Page 34

CHAPTER V.

WEIGHT OF BODIES. — EQUILIBRIUM OF HEAVY BODIES. — CENTRE OF GRAVITY. —

THE BALANCE.

Distinction between the weight of a body and its mass — Loss of weight which a
body undergoes when it is taken from the poles to the equator — Centre of
gravity, in bodies of geometric form ; in bodies of irregular form — The Balance ;
conditions of accuracy and sensibility — Balance of precision — Method of double
weighing — Specific gravity and density of bodies . Page. 45

CHAPTER VI.

WEIGHT OF LIQUIDS. — PHENOMENA AND LAWS OF EQUILIBRIUM: HYDROSTATICS.

Difference of constitution of solids and liquids ; molecular cohesion — Flowing of
sand and powders — Mobility of the molecules of liquid bodies — Experiments
of the Florentine Academicians ; experiments of modern philosophers — Pascal's
law of equal pressures — Horizontality of the surface of a liquid in equilibria —
Pressure on the bottom of vessels ; pressures normal to the sides ; hydraulic
screw — Hydrostatic paradox ; Pascal's bursting-cask — Equilibrium of super-
posed liquids ; communicating vessels Page 58

CHAPTER VII.

EQUILIBRIUM OF BODIES IMMERSED IN LIQUIDS. — PRINCIPLE OF ARCHIMEDES.

Pressure or loss of weight of immersed bodies — Principle of Archimedes — Experi-
mental demonstration of this principle — Equilibrium of immersed and floating
bodies — Densities of solid and liquid bodies ; Areometers .... Page 73

CHAPTER VIII.

WEIGHT OF THE AIR AND OF GASES. — THE BAROMETER.

The air a heavy body — Elasticity and compressibility of air and other gases —
Pneumatic or fire syringe — Discovery made by Florentine workmen — Nature
abhors a vacuum — Experiments of Torricelli and Pascal — Invention of the
barometer — Description of the principal barometers . . . . » . Page 84

CONTENTS.

CHAPTER IX.

WEIGHT OF THE AIR AND OF GASES (continued). — PUMPS. — MARIOTTfi's LAW. — •

THE AIR-PUMP.

Principle of the ascent of liquids in pumps — Suction and force pumps — The
siphon — Air-pump ; principle of its construction — Double and single barrel
air-pumps — Condensing pumps — Mariotte's law Page 102

BOOK II.

SOUND.
CHAPTER I.

THE PHENOMENA OF SOUND Poge 123

CHAPTER II.

PRODUCTION AND PROPAGATION OF SOUND. — REFLECTION OF SOUND. — VELOCITY
OF SOUND IN DIFFERENT MEDIA.

Production of sound by a blow or percussion, and by friction, in solids, liquids, and
gases — Production of sound by the contact of two bodies at different tem-
peratures ; Trevelyan's instrument — Chemical harmonicon — The air a vehicle
of sound ; transmission of sound by other gases, by solids and liquids — Pro-
pagation of sound at great distances through the intervention of the ground —
Velocity of sound through air ; influence of temperature ; experiments of
Villejuif and Montlhery — Velocity of sound in water ; experiments made on
the Lake of Geneva, by Colladon and Sturm— Velocity of sound through
different solid, liquid, and gaseous bodies Page 126

CHAPTER III.

PROPAGATION OF SOUND. — PHENOMENA OF THE REFLECTION AND REFRACTION

OF SOUND.

Echoes and resonances — Simple and multiple echoes ; explanation of these
phenomena— Laws of the reflection of sound : experimental verification-
Phenomena of reflection at the surface of elliptical vaults— Experiments
which prove the refraction of sonorous impulses Page 138

CHAPTER IV.

SONOROUS VIBRATIONS.

Experiments which prove that sound is produced by the vibratory movement of the
particles of solid, liquid, and gaseous bodies — Vibrations of a cord, rod, or bell
Trevelyan's instrument — Vibrations of water and of a column of air — Nature

xii CONTENTS.

of sound : pitch, intensity, and clang-tint — The pitch depends on the number
of vibrations of the sounding body ; Savart's toothed wheel ; Cagniard-Latour's
and Seebeck's syrens — Graphic method —Variable intensity of sound during
the day and night — Limit of perceptible sounds ... ... Page 145

CHAPTER V.

LAWS OF SONOROUS VIBRATIONS, IN STRINGS, RODS, PIPES, AND PLATES.

Experimental study of the laws which govern the vibration of strings — Monochord
or Sonometer — Nodes and ventral segments ; harmonics — Laws of the vibra-
tions of sonorous pipes — Vibrations in rods and plates— Nodal lines of square,
round, and polygonal plates Page 163

CHAPTER VI.

PROPAGATION OF SOUND IN AIR.— SOUND WATES.

Nature of sound waves ; their propagation in a tube — The wave of condensation
and the wave of rarefaction — Length of sonorous undulations — Propagation
through an unlimited medium ; spherical waves ; diminution of their amplitude
with the distance — Direction of sound waves — Co-existence of undulations —
Perception of simultaneous sounds ; Weber's experiments .... Page 178

.CHAPTER VII.

MUSICAL SOUNDS. — THE GAMUT, OR MUSICAL SCALE.

Distinction between noises and musical sounds — Definition of the gamut ; intervals
which compose it — The scale of the musical gamut is unlimited ; convention
which limits it in practice — Names and values of the intervals of the natural
major scale — Modulations ; constitution of the major scales proceeding by
sharps and flats — Minor scale Page 185

CHAPTER VIII.

OPTICAL STUDY OF SOUNDS.

Vibrations of a tuning-fork ; the sinuous curve by which they are represented —
Appreciation of the comparative pitch of two notes by the optical method of
M. Lissajous — Optical curves of the different intervals of the scale ; differences
of phase — Determination of the concord of two tuning-forks — Vibrations of
columns of air in tubes ; manometric flames, M. Koenig's method — Comparative
study of the sounds given out by two tubes ; the nodes and ventral segments of
columns of air Page 193

CHAPTER IX.

QUALITY OF MUSICAL NOTES.

Simple and compound notes — Co-existence of harmonics with the fundamental
notes — The quality (clang-tint) of a note depends on the number of the harmonics
and their relative intensity : M. Helmholtz's theory — Harmonic resonant
chambers (resonnateurs) ; experimental study of the quality of musical notes —
Quality of vowels Page 204

CONTENTS.

CHAPTEK X.

HEARING AND THE VOICE.

Organ of hearing in man ; anatomical description of the ear — The external ear ; the
orifice and auditory meatus — The intermediate ear; the drum and its membrane;
chain of small bones — The internal ear or labyrinth ; semicircular canals, the
cochlea and fibres of Corti ; auditory nerve — Role of these different organs in
hearing ; the difference between hearing and listening — The organ of the voice
in man ; larynx, vocal cords — Clang-tint of voices Page 208

BOOK III.

LIGHT.
CHAPTER I.

SOURCES OF LIGHT ON THE SURFACE OF THE EARTH.

Sources of cosmical light : the sun, planets, and stars— Terrestrial, natural, and
artificial luminous sources— Lightning ; Polar aurorse : electric light ; volcanic
fires ; light obtained by combustion Page 219

CHAPTER II.

THE PROPAGATION OF LIGHT IN HOMOGENEOUS MEDIA.

Light is propagated in vacuo — Transparent, solid, liquid, and gaseous bodies ;
transparency of the air — Translucid bodies — Light is propagated in a right line
in homogeneous media ; rays, luminous pencils, and bundles of rays — Cone of
shadow, broad shadow, cone of penumbra — The camera obscura — Light is not
propagated instantaneously — Measure of the velocity of light by the eclipse of
Jupiter's satellites — Methods of MM. Fizeau and Foucault . . . Page 221

CHAPTER III.

PHOTOMETRY. — MEASURING THE INTENSITY OF LIGHT SOURCES.

Luminous intensity of light sources, illuminating power — Principles of photometry
— Law of distances — Law of cosines — Rumford's photometer — Bouguer's photo-
meter— Determination of the illuminating power of the Sun and the full Moon
—Stellar photometer ' . Page 238

CONTENTS.

CHAPTER IV.

REFLECTION OF LIGHT.

Phenomena of reflection of light — Light reflected by mirrors ; diffused light ; why
we see things — Path of incident and reflected rays ; laws of reflection — Images
in plane mirrors — Multiple images between two parallel or inclined surfaces ;
kaleidoscope — Polemoscope ; magic lantern — Spherical curved mirrors ; foci
and images in concave and convex mirrors — Caustics by reflection — Conical and
cylindrical mirrors — Luminous spectres . ." Page 247

CHAPTER V.

REFRACTION OF LIGHT.

Bent stick in water ; elevation of the bottoms of vessels — Laws of the refraction
of light ; experimental verification — Index of refraction — Total reflection —
Atmospheric refraction ; distortion of the sun at the horizon . . . Page 275

CHAPTER VI.

REFRACTION OF LIGHT. — PRISMS AND LENSES.

Transparent plates with parallel faces ; deviation of luminous rays — Multiple
images in a silvered mirror — Prisms — Phenomena of refraction in prisms — •
Converging and diverging lenses — Real and virtual foci of converging lenses ;
real and virtual images — Foci and images of diverging lenses — Dark chamber —
Megascope — Magic lantern and phantascope — Solar microscope . . Page 286

CHAPTER VII.

COLOURS : THE COLOURS IN LIGHT SOURCES, AND IN NON-LUMINOUS BODIES. —
DISPERSION OF COLOURED RAYS.

White colour of the sun's light — Decomposition of white light into seven simple
colours ; solar spectrum — Reconiposition of white light by the mixture of the
coloured rays of the spectrum — Newton's experimenl ; unequal refrangibility
of simple rays — Colours of non-luminous bodies Page 306

CHAPTER VIII.

COLOURS.

Classification of colours — Tones and scale of the colours of the solar spectrum, after
the method of M. Chevreul — Chromatic circles of pure and subdued colours ;
tones and scales — Complementary colours Page 317

CHAPTER IX.

LINES OF THE SOLAR SPFCTRUM.

The discoveries of Wollaston and Fraunhofer ; dark lines distributed through the
different parts of the solar spectrum — Spectral lines of other luminous sources —
Spectrum analysis ; spectrum of metals ; inversion of the spectra of flames —
Chemical analysis of the atmosphere of the sun, of the light of stars, nebuke,
and comets Page 323

CONTENTS.

CHAPTER X.

SOLAR RADIATIONS. — CALORIFIC, LUMINOUS, AND CHEMICAL.

Divisions of the spectrum ; maximum luminous intensity of the spectrum — Obscure
or dark rays ; heat rays ; chemical rays — Fluorescence, calorescence.

Page 336

CHAPTER XI.

PHOSPHORESCENCE.

Phenomena of spontaneous phosphorescence — Animal and vegetable phosphores-
cence— Glow-worms and fulgurse ; infusoria and medusae — Different conditions
which determine the phosphorescence of bodies — Phosphoresence by inso-
lation— Becquerel's phosphoroscope . . . Page 341

CHAPTER XII.

WHAT IS LIGHT?

Hypotheses concerning the nature of light — Newton's emission theory — Huyghens'
undulatory theory ; vibrations of the ether — Propagation of luminous waves ;
wave-lengths of the different rays of the spectrum ...... Page 348

CHAPTER XIII.

INTERFERENCE OF LUMINOUS WAVES. — PHENOMENA OF DIFFRACTION. — GRATINGS.

Dark and bright fringes due to very small apertures — Grimaldi's experiment —
Interference of luminous waves ; experimental demonstration of the principle of
interference — Phenomena of diffraction produced by slits, apertures of different
form and gratings — Coloured and monochromatic fringes .... Page 357

CHAPTER XIV.

COLOURS OF THIN PLATES.

The soap-bubble — Iridescent colours in thin plates — Newton's experiment on
coloured rings ; bright and dark rings — Laws of diameters and thicknesses —
Coloured rings are phenomena of interference — Analysis of the colours of the
soap-bubble Page 367

CHAPTER XV.

DOUBLE REFRACTION OF LIGHT.

Discovery of double refraction by Bartholin — Double images in crystals of
Iceland spar — Ordinary and extraordinary rays ; principal section and optic
axis — Positive and negative crystals — Bi-refractive crystals with two axes,
or bi-axial crystals Page 376

xvi CONTENTS.

CHAPTER XVI.

POLARIZATION OF LIGHT.

Equal intensity of the ordinary and extraordinary images in a doubly refracting
crystal — Natural light — Huyghens' experiments ; variations of intensity with
four images ; polarized light — Polarization of the ordinary ray ; polarization
of the extraordinary ray : the two planes in which these polarizations take place
—Polarization by reflection Page 385

CHAPTER XVII.

CHROMATIC POLARIZATION.

Discovery of the colours of polarized light, by Arago — Thin plates of doubly
refractive substances ; variations of colours according to the thickness of the
plates — Colours shown by compressed and heated glass — Coloured rings in
crystals with one or with two axes — Direction of luminous vibrations : they are
perpendicular to the direction of propagation, or parallel to the surface of the
waves Page 397

CHAPTER XVIII.

THE EYE AND VISION.

Description of the human eye — Formation of - images on the retina— Distinct
vision of the normal eye — Conformation of the eyes in Myopsis and
Presbyopsis Page 406

BOOK IY.

HEAT.
CHAPTER I.

DILATATION. — THERMOMETERS.

Sensations of heat and cold ; causes of error in the perception of the temperature
of bodies — General phenomena of dilatation and contraction in solids, liquids,
and gases — Temperature of bodies — Thermometers based on dilatation and
contraction — The mercurial thermometer — Alcohol thermometer— Air ther-
mometers ; metallic thermometers Page 415

CHAPTER II.

MEASURE OF EXPANSION.

Effects of variations of temperature in solids, liquids, and gases. — Applications to
the arts — Rupert's drops — Measure of the linear expansion of solids — Expan-
sion of crystals — Contraction of iodide of silver — Absolute and apparent ex-
pansion of liquids — All gases expand to the same extent between certain limits
of temperature Page 432

CONTENTS. xvii

CHAPTER III.

EFFECTS OF VARIATIONS OF TEMPERATURE : CHANGES IN THE STATE OF BODIES.

The passage of bodies from a solid to a liquid state : fusion — Return of liquids to
the solid state : solidification or congelation — Equality of the temperatures of
fusion and solidification — Passage of liquids into gases : difference between
evaporation and vaporization — Phenomenon of ebullition : fixed temperature
of the boiling-point of a liquid under a given pressure — Return of vapours
and gases into a liquid condition : liquefaction and congelation of carbonic
acid and several other gases — A permanent gas defined Page 443

CHAPTER IV.

PROPAGATION OF HEAT. — RADIANT HEAT.

Heat is transmitted in two different ways, by conduction and by radiation —
Examples of these two modes of propagation — Radiation of obscure heat in
vacua — Radiant heat is propagated in a straight line ; its velocity is the same
as that of light — Laws of the reflection of heat ; experiments with conjugate
mirrors — Apparent radiation of cold — Burning mirrors — Refraction of heat;
burning glasses — Similarity of radiant heat and of light — Study of radiators,
reflectors, absorbing and diathermanous bodies — Thermo-electric pile ; experi-
ments of Leslie and Melloni Page 457

CHAPTER V.

TRANSMISSION OF HEAT BY CONDUCTION.

Slow transmission of heat in the interior of bodies — Unequal conductivity of
solids — Conductivity of metals, crystals, and non-homogeneous bodies — Pro-
pagation of heat in liquids and gases ; it is principally effected by transport or
convection — Slight conductivity of liquid and gaseous bodies . . Page 477

CHAPTER VI.

CALORIMETRY. — SPP:CIFIC HEAT OF BODIES.

Definition of a unit of heat — Heat absorbed or disengaged by bodies during varia-
tions in their temperature — Specific heat of solids — Latent heat of fusion —
Ice-calorimeter — Latent heat of vaporization of water .... Page 484

CHAPTER VII.

SOURCES OF HEAT.

Solar heat ; measure of its intensity at the surface of the earth, and at the limits
of the atmosphere ; total heat radiated by the sun — Temperature of space
— Internal heat of the globe — Heat disengaged by chemical combinations ;
combustion — Heat of combustion of various simple bodies — Production of
high temperatures by the use of the oxyhydrogen blowpipe — Generation of
heat by mechanical means ; friction, percussion, compression « , Page 492

xviii CONTENTS.

CHAPTER VIII.

HEAT A SPECIES OF MOTION.

What we understand by the mechanical equivalent of heat — Joule's experiments
for determining this equivalent — Reciprocal transformation of heat into
mechanical force, and of mechanical force into heat — Heat is a particular
kind of motion . Page 504

BOOK Y.

MAGNETISM.

CHAPTER I.

MAGNETS.

Phenomena of magnetic attraction and repulsion — Natural and artificial magnets ;
magnetic substances — Poles and neutral line in magnets — Action of magnets
on magnetic substances ; action of magnets on magnets — Law of magnetic
attraction and repulsion — Direction of the magnetic needle : declination and
inclination; influence of the terrestrial magnet — Process of magnetization —
Attractive force of magnets Page 511

BOOK VI.

ELECTRICITY.
CHAPTER I.

ELECTRICAL ATTRACTION AND REPULSION.

Attraction of amber for light bodies— Gilbert's discoveries ; electricity developed
by the friction of a number of bodies— Study of electrical attraction and repul-
sion ; insulators, or bad conductors ; good conductors — Electrical pendulum —
Resinous and vitreous, positive and negative electricity — Laws of electrical
attraction and repulsion — Distribution of electricity on the surface of bodies —
Influence of points \* ' ' Pa9e 5'31

CHAPTER II.

ELECTRICAL MACHINES.

CONTENTS.

positive and negative electricities — Electroscopes ; electric pendulum ; dial
and gold-leaf electroscopes — Electrical machines : Otto von Guericke's machine ;
Ramsden, or plate-glass machines ; machines of Nairne and Armstrong — The
electrophorus Page 545

CHAPTEE III.

LEYDEN JAR. — ELECTRICAL CONDENSERS.

The experiments of Cuneus and Muschenbroeck ; discovery of the Leyden jar —
Theory of electrical condensation ; the condenser of ^Epinus — Jar with moveable
coatings— Instantaneous and successive discharges — Leichtenberg's figures —
Electric batteries — The universal discharger — Apparatus for piercing a card
and glass — Transport and volatilization of metals; portrait of Franklin —
Chemical effects of the discharge ; Volta's pistol — Fulminating pane.

Page 567

CHAPTER IV.

THE PILE OR BATTERY. — ELECTRICITY DEVELOPED BY CHEMICAL ACTION.

Experiments of Galvani and discoveries of Volta ; condensing electrometer —
Description of the upright pile — Electricity developed by chemical actions —
Theory of the pile ; electro-motive force ; voltaic current — Electricities of high
and low tension — Couronne de tasses ; Wollaston's pile ; helical pile — Constant-
current piles ; Daniell, Bunsen, and Grove elements — Physical, chemical, and
physiological effects of the pile — Experiments with dead and living animals.

Page 585

CHAPTER V.

ELECTRO-MAGNETISM.

Action of a current on the magnetic needle ; Oersted and Ampere — Schweigger's
multiplier ; construction and use of the galvanometer — Action of magnets on
currents — Action of currents on currents — Influence of the terrestrial magnetic
force — Ampere's discoveries ; solenoids ; the electrical helix ; theory of magnets
— Magnetism of soft iron or steel discovered by Arago ; magnetization by means
of helices — The electro-magnet ; its magnetic power ; its effects . Page 604

CHAPTER VI.

PHEONMENA OF INDUCTION.

Discovery of induction by Faraday— Induction by a current ; inducing coil and
induced coil — Induction by a magnet — Machines founded on the production of
induced currents — Clarke's machine — Ruhmkorff's machine — Commutator —

Effects of the induction coil Page 620

b 2

xs CONTENTS.

CHAPTER VIT.

THE ELECTRIC LIGHT.

Sparks obtained by static electrical discharges ; luminous tufts — Light in rarefied
gases — Voltaic arc ; phenomena of transport ; form of the carbon points —
Intensity of the electric light — Electric light of induction currents — Stratifi-
cations ; experiments with Geissler's tubes — Phosphorescence of sulphate of
quinine Page 631

BOOK VII.

• ATMOSPHERIC METEORS.

Optical meteors ; mirage, rainbow — Tension of aqueous vapour in the atmosphere ;
hygrometry — Clouds and fogs — Dew, rain, snow — Crystals of snow and ice —
Variations of barometric pressure — Measure of maxima and minima tempe-
ratures— Electrical meteors ; thunderbolts, thunder and lightning — Aurora
boreales Page 645

APPENDIX.

DISCOVERY OF OXYGEN IN THE SUN BY PHOTOGRAPHY, AND A NEW THEORY
OF THE SOLAR SPECTRUM Page 673

•
INDEX " Page 685

COLOURED PLATES.

PAGE

I. POLAR AURORA BOREALIS (Front.) 521

II. SPECTRA OF DIFFERENT LIGHT SOURCES ... 352

III. SPECTRUM SHOWING OXYGEN AND NITROGFN IN THE SUN 673

LIST OF ILLUSTRATIONS ON WOOD.

FIG. PAOF

1. Action of weight shown by the tension of a spring 4

2. Convergence of the verticals towards the centre of the earth .... 11

3. Tke Leaning Tower at Pisa 17

4. Experiment showing the equal velocity of bodies falling in vacuo ... 10

5. The direction of gravity is perpendicular to the surface of liquids at rest 21

6. Eastern deviation in the fall of bodies 23

7. Movement of heavy bodies on an inclined plane 24

8. Pulley of Attwood's machine 25

9. Experimental study of the laws of falling bodies. Attwood's machine . 26

10. Experimental study of falling bodies. Law of spaces described ... 27

11. Experimental study of falling bodies. Law of velocity 29

12. M. Morin's machine 30

13. Parabola described by the weight in its fall 31

14. Oscillatory movement of a simple pendulum 36

15. Compound pendulum 38

16. Effect of centrifugal force 40

17. Borda's pendulum. Platinum sphere and knife-edge 41

18. Borda's pendulum. Measurement of the time of an oscillation by the

method of coincidences 42

19. Weight of a body ; centre of gravity 45

20. Centres of gravity of parallelograms, a triangle, a circle, a circular ring,

and an ellipse 47

21. Centres of gravity of a prism, pyramid, cylinder, and cone 48

22. Centres of gravity of an ellipsoid and a sphere of revolution .... 48

23. Experimental determination of the centre of gravity of a body of

irregular form or non-homogeneous structure 49

24. Equilibrium of a body supported on a plane by one or more points . . 50

25. Equilibrium of a body resting on a plane by three supports 50

26. Positions of equilibrium of persons carrying loads 51

27. Equilibrium on an inclined plane 51

28. Stable, neutral, and unstable equilibrium 52

29.- Scales 53

3D. Chemical balance : the beam 54

31. Chemical balance 55

32. Flowing of sand 59

xxiv LIST OF ILLUSTRATIONS.

FTQ.

33. Cohesion of liquid molecules 60

34. Spherical form of dew-drops 60

35. Cohesion of liquid molecules ; drops of mercury 61

36. Principle of the hydraulic press ; 62

27. The pressure exercised on one point of a liquid is transmitted equally in

every direction 63

38. The surface of liquids in repose is horizontal 63

39. Pressure of a liquid on the bottom of the vessel which contains it . . 64

40. Pressure of a liquid on the bottom of a vessel : Haldat's instrument . . 66

41. Pressure of a liquid on a horizontal stratum 67

42. The pressures of liquids are normal to the walls of the containing vessel 67

43. Hydraulic tourniquet 68

44. Hydrostatic paradox 68

45. Hydrostatic paradox. Pascal's experiment 69

46. Equilibrium of superposed liquids of different densities 70

47. Equality of height of the same liquid in communicating vessels ... 71

48. Communicating vessels. Heights of two liquids of different densities . 72

49. Experimental demonstration of the principle of Archimedes .... 74

50. Principle of Archimedes. Reaction of one immersed body on the liquid

which contains it .*».....,,... 75

51. Equilibrium of a body immersed in a liquid of the same density as

its own 78

52. Density of solid bodies. Method of the hydrostatic balance .... 79

53. Density of solid bodies. Charles' or Nicholson's areometer 80

54. Density of solid bodies. Method of the specific gravity bottle ... 81

55. Density of liquids. Hydrostatic balance 81

56. Specific gravity of liquids. Fahrenheit's areometer 82

57. Specific gravity of liquids. Method of the specific gravity bottle . . 82

58. Experimental demonstration of the weight of air and other gases ... 86

59. Elasticity and compressibility of gases 87

60. Pneumatic syringe 88

61. Torricelli's experiment 90

62. Torricelli's experiment. Effect of the weight of the atmosphere ... 90

63. Magdeburg hemispheres 92

64. Bursting a bladder by exhausting the air underneath it 92

65. Jet of water in vacua 93

66. Normal or standard barometer 95

67. An ordinary cistern barometer 95

68. Cistern of Fortin's barometer 96

69. Fortin's barometer as arranged for travelling 97

70. Gay-Lussac's barometer, modified by Bunten 98

71. Pial or wheel barometer 99

72. Bourdon's aneroid barometer 100

73. Vidi's aneroid barometer 101

74. Principle of the suction-pump 103

75. Suction-pump 104

76. Force-pump 105

77. Combined suction- and force-pump 105

LIST OF ILLUSTRATIONS. XXv

*•«»' PAGE

78. The siphon 106

79. Action of the piston and valves in the air-pump 108

80. Detail of the piston and its valves * .... 109

81. Air-pump with two cylinders. Transverse section 109

82. Plan of the air-pump with two cylinders 110

83. Exterior view of the air-pump Ill

84. Bianchi's air-pump. Interior view of the cylinder 112

85. Bianchi's air-pump. General view 113

86. The baroscope 115

87. Condensing machine. Interior view of the piston 115

88. Silbermann's condensing pump. Exterior view 116

89. Silbermann's condensing pump. Section 116

90. Connected condensing pumps 117

91. Experimental proof of Mariotte's law 118

92. Philosophical lamp or chemical harmonicon 128

93. Sound is not propagated in a vacuum 129

94. Measure of the velocity of sound through air, between Villejuif and

Montlhery, in 1822 132

95. Experimental determination of the velocity of sound through water . 135

96. Experiments made on the Lake of Geneva, by Colladon and Sturm . 136

97. Reflection of sound. Phenomena of resonance 139

98. Property of the parabola 141

99. Experimental study of the laws of the reflection of sound 142

100. Reflection of sound from the surface of an elliptical roof 143

101. Sonorous refraction. M. Sondhauss's instrument 144

102. Vibrations of stretched string 146

103. Vibrations of a metal rod 147

104. Proof of the vibration of a glass bell 148

105. Vibrations of a metal clock-bell 149

106. Trevelyan's instrument 149

107. Trevelyan's instrument. Cause of vibratory movements 150

108. Vibrations of liquid molecules 150

109. Vibrations of a gaseous column 151

110. Savart's toothed wheel. Study of the number of vibrations producing

sounds of a given pitch 152

111. Cagniard-Latour's Syren 153

112. Interior view of the Syren 153

113. Seebeck's Syren 154

114. Graphic study of the sonorous vibrations. Phonautography .... 155

115. Combination of two parallel vibratory movements ........ 156

116. Combination of two rectangular vibratory movements 157

117. Sonometer 164

118. Harmonic sounds. Nodes and ventral segments of a vibrating string . 167

119. Harmonics. Nodes and ventral segments of a vibrating string . . . 168

120. Vibrations of compound sounds 169

121. Prismatic sonorous pipes 170

122. Cylindrical sonorous pipes 170

123. Tubes of similar forms . , 171

LIST OF ILLUSTKATIONS.

FIG.

124. Sonorous tubes. Laws of the vibrations of open and closed tubes of

different lengths 172

125. Longitudinal vibrations of rods 174

126. Vibrations of a plate 1*75

127. Nodal lines of vibrating square plates, according to Savart .... 176

128. Nodal lines of vibrating circular or polygonal plates, according to

Chladni and Savart 177

129. Nodes and segments of a vibrating bell 177

130. Propagation of the sonorous vibrations in a cylindrical and unlimited

gaseous column 179

131. Curve representing a sound wave 179

132. Propagation of a sonorous wave through an unlimited medium . . . 181

133. Experiment proving the co-existence of waves. Propagation and reflec-

tion of liquid waves on the surface of a. bath of mercury .... 183

134. A tuning-fork mounted on a sounding-box 194

135. Optical study of vibratory movements 196

136. Optical curves representing the rectangular vibrations of two tuning-

forks in unison 197

137. Optical curves. The octave, fourth and fifth . 197

138. Open tube with manometric flames 199

139. Manometric flames. Fundamental note, and the octave above the

fundamental note 200

140. Apparatus for the comparison of the vibratory movements of two

sonorous tubes 201

141. Manometric flames simultaneously given by two tubes at the octave . 202

142. Manometric flames of two tubes of a third 202

143. M. Helinholtz'a resonance globe 205

144. M. Koenig's apparatus for analysing clang-tints 206

145. The human ear ; section of the interior tympanum ; chain of small

bones. Internal ear ; labyrinth 210

146. Details of the auditory ossicles 211

147. Section of the cochlea 211

148. Auditory apparatus of fishes ; ear of the Ray 212

149. The human voice ; interior view of the larynx. Glottis ; vocal chords 213

150. Propagation of light in a right line 224

151. Rectilinear propagation of light 224

152. Cone of shadow of an opaque body. Completed shadow 225

153. Cones of umbra and penumbra 226

154. Silhouettes of perforated cards ; ei^ect of the umbra and penumbra . 227

155. Inverted image of a candle 228

156. Images of* the sun through openings in foliage . 229

157. Dark chamber. Reversed image of a landscape 230

158. Measure of the velocity of light by the eclipses of Jupiter's satellites . 232

159. M. Fizeau's instrument for the direct measure of the velocity of light . 235

160. Measure of the velocity of light by M. Fizeau 236

161. Law of the square of distances 241

162. Rumford's photometer 1 243

163. Bouguer's photometer , , , 244

LIST OF ILLUSTRATIONS.

FIQ.

164. Phenomena of reflection 249

165. Experimental study of the laws of the reflection of light 251

166. Reflection from a plane mirror. Form and position of the images . . 252

167. Reflection from a plane mirror. Field of the mirror 253

168. Reflections from two plane parallel mirrors. Multiple images ... 254

169. Images on two mirrors inclined at right angles to each other .... 255

170. Images, in mirrors at right angles (90°) 255

171. Images in mirrors at 60° 255

172. Images in mirrors at 45° 256

173. Symmetrical images formed in the kaleidoscope 256

174. Polemoscope 257

175. Magic telescope 258

176. Concave mirror. Inverted image, smaller than the object 259

177. Concave mirror. Inverted images, larger than the object 260

178. Concave mirror. Virtual images, erect and larger than the object . . 261

1 79. Concave mirror. Path and reflection of rays parallel to the axis. Prin-

cipal focus 262

180. Concave mirror. Conjugate foci 263

181. Concave mirror. Virtual focus 263

182. Concave mirror. Real and inverted image of objects 264

183. Concave mirror. Erect and virtual image of objects 264

184. Upright virtual image in convex spherical mirror 265

185. Convex mirror. Erect and virtual image 266

186. Caustic by reflection 266

187. Caustic by reflection * 267

188. Cylindrical mirror. Anamorphosis 267

189. Reflection on conical mirrors. Anamorphosis 268

190. Light reflected very obliquely 269

191. Irregular reflection or scattering of light on the surface of an unpolished

body 270

192. The Ghost (produced by reflection) 271

193. Arrangement of the unsilvered glass- and the position of the Ghost . . 273

194. Phenomena of refraction of light. The bent stick 275

195. Refraction of light. Apparent elevation of the bottoms of vessels . . 276

196. Experimental demonstration of the laws of refraction 278

197. Law of sines 279

198. Explanation of the bent stick 280

199. Apparent elevation of the bottoms of vessels ; explanation .... 280

200. Total reflection. Limiting angle 281

201. Phenomenon of total reflection 282

202. Phenomenon of total reflection, in the shutter of a camera obscura . . 283

203. Atmospheric refraction. The effect on the rising and setting of stars . 284

204. Normal view. ) Deviation due to refraction through plates with )

205. Oblique view. ) parallel faces )

206. Path of a luminous pencil 287

207. Multiple images produced by refraction in plates with parallel faces . 288

208. Path of the rays which give place to the multiple images of plates with

parallel faces . 288

xxviii LIST OF ILLUSTKATIONS.

Fia. PAGE

209. Geometrical form of the prism 288

210. Prism mounted on a stand 288

211. Deviation of luminous rays by prisms 289

212. Images of objects seen through prisms 290

213. Magnifying glass or lens with convex surfaces, side and front view . . 291

214. Converging lenses. — Bi-convex lens ; plano-convex lens ; converging

meniscus 292

215. Diverging lenses. — Bi-concave lens , plano-concave lens ; diverging

meniscus 292

216. Secondary axes of lenses. Optical centre . . :.-,,.. ...... 293

217. Path of rays parallel to the axis. Principal focus 294

218. The lens may be considered as an assemblage of prisms 295

219. Path of rays emanating from a luminous point on the axis. Conjugate

foci 296

220. Path of rays emanating from a point situated between the principal

focus and the lenses. Virtual focus 296

221. Eeal image, inverted and smaller than the object 297

222. Eeal image, inverted and larger than the object 298

223. Image of an object situated at a distance from the lens greater than the

principal focal distance, and less than double that distance . . . 298

224. Erect and virtual images of an object placed between the principal

focus and the lens 299

225. Principal virtual focus of diverging lenses 299

226. Erect virtual images, smaller than the object in a bi-concave lens . . 300

227. Camera obscura 301

228. Lens-prism of the camera obscura 302

229. Megascope 302

230. Magic lantern 303

231. Phantascope 304

232. Solar microscope, complete 304

233. Section of the solar microscope 305

234. Decomposition of light by the prism. Unequal refrangibility of the

colours of the spectrum 307

235. Recomposition of light by a lens 309

236. Recomposition of light by prisms 310

237. Recomposition of white light by a revolving disc 311

238. Unequal refrangibility of various colours 312

239. Unequal refrangibilities of simple colours. Newton's experiment . . 313

240. A fragment of the solar spectrum 325

241. Spectroscope 327

242. M. Ed. Becquerel's phosphoroscope 345

243. Disc of the phosphoroscope 346

244. Grimaldi's experiment. Dark and bright fringes produced by a system

of two small circular holes ,* • . .-. . . 358

245. Interference of luminous waves 358

246. Fresnel's experiment of two mirrors ; experimental demonstration of

the principles of interference ,.*,%. . 360

247. Effects of diffraction in telescopes. (Sir J. Herschel) 363

LIST OF ILLUSTRATIONS. xxix

FIG. PAG 8

248. Strise of mother-of-pearl seen with a magnifying power of 20,000

diameters 365

249. Thin plate of air comprised between two glasses, one plane, the other

convex. (Newton's experiment of coloured rings) 369

250. Newton's coloured rings 369

251. Colours of thin plates in the soap-bubble 373

252. Specimen of Iceland spar 377

253. Double images of objects seen through a crystal of Iceland spar . . . 378

254. Positions of the extraordinary image in relation to the plane of incidence.

Principal section 380

255. Principal sections and optic axis of Iceland spar 380

256. Artificial section perpendicular to the optic axis 381

257. Crossing of the rays which produce the ordinary and extraordinary image 381

258. Eock crystal 383

259. Propagation of ordinary and extraordinary images of a double refracting

crystal. Equal intensity 386

260. Equal intensity of ordinary and extraordinary images 386

261. Huyghens' experiment. Variations in intensity of the images seen

when one prism of Iceland spar is rotated over another 387

262. Polarization of the ordinary ray by double refraction 388

263. Division of the ordinary ray. Variable intensities of the images of the

polarized rays 389

264. Division of the extraordinary ray. Intensities of the images of the

polarized rays 389

265. Specimen of Siberian tourmaline 391

266. The polariscope of Malus perfected by JVL Biot 394

267. Eelation between the polarized ray and the angle of polarization of a

substance and the refracted ray 395

268. Colours of polarized light in compressed glass 399

269. Colours of polarized light in unannealed glass 400

270. Pincette of tourmaline 401

271. Horizontal section of the eyeball 407

27 la. Diagrammatic views of the nervous and the connective elements of the

retina, supposed to be separated from one another 409

272. Formation of images in the normal eye 410

273. Formation of the image in the eye of a long-sighted person .... 411

274. Formation of the image in the eye of a short-sighted person .... 411

275. S'Gravesande's ring. Expansion of solids by heat 417

276. Expansion of solids 417

277. Linear expansion of a solid rod 418

278. Expansion of liquids by heat 419

279. Expansion of gases by heat 419

280. Expansion of gases 420

281. Eeservoir and tube of the mercurial thermometer 421

282. Determination of the zero in the mercurial thermometer ; temperature

of fusion of ice 422

283. Determination of the point 100°, the temperature of boiling water

under a pressure of 760 millimetres , , 423

LIST OF ILLUSTRATIONS.

FIG. PAGE

284. Centigrade thermometers with their graduated scales 424

285. Thermometrical scales 425

286. Air thermometers of Galileo and Cornelius Drebbel 427

287. Differential thermometers of Leslie and Rumford . 428

288. Unequal expansion of two different metals for the same elevation of

temperature 429

289. Metallic dial thermometer 430

290. Breguet's metallic thermometer 430

291. Room of the Conservatoire des Arts et Metiers. Walls rectified by

force of contraction „ 434

292. Dutch tears 435

293. Measure of the linear expansion of a solid, by the method of Lavoisier

and Laplace 436

294. Laplace and Lavoisier's instrument for the measure of linear expansion 437

295. Experiment proving the contraction of water from 0° to 4° .... 441

296. Effects of expansion produced by the freezing of water 447

297. Ebullition in open air 449

298. Papin's digester 450

299. Ebullition of water at a temperature lower than 100° 451

300. Spontaneous evaporation of a liquid in the barometric vacuum. First

law of Dalton 452

301. Invariability of the maximum tension of the same vapour at the same

temperature. Dalton's second law 453

302. Inequalities of the maximum tensions of different vapours at the same

temperature. Dalton's third law 454

303. Radiation of obscure heat in vacua 459

304. Reflection of heat ; experiments with parabolic conjugate mirrors . . 460

305. Burning mirror 462

306. Refraction of heat . 463

307. Echelon lens . . . 464

308. Measure of the emissive powers of bodies. Experiment with Leslie's cube 466

309. Elements of the thermo-electric pile 468

310. Thermo-electric pile for the study of the phenomena of heat .... 469

311. Apparatus used by Melloni to measure the reflecting powers of bodies 470

312. Melloni's apparatus for measuring the diathermanous power of bodies . 474

313. Cube of boiling water 474

314. Plate of blackened copper heated to 400° 474

315. Incandescent spiral of platinum 474

316. Intensity of radiant heat. Law of the squares of the distances . . . 476

317. Unequal conductivities of copper and iron 478

318. Ingenhouz' apparatus for measuring conducting powers 478

319. Experiment on the conductivity of iron compared with that of bismuth 480

320. Unequal conductivity of quartz in different directions 480

321. Property of metallic gauze ; obstacle which it opposes to the propagation

of heat 482

322. Measure of the specific heat of bodies . Simple ice calorimeter . . . 490

323. Measure of the specific heat of bodies by the ice calorimeter of Laplace

and Lavoisier . .... 490

LIST OF ILLUSTRATIONS. xxxi

FIO. PAOE

324. M. Pouillet's Pyrhelioraeter . 494

325. Combustion of iron in oxygen 497

326. Flame of a candle 498

327. Oxyhydrogen blowpipe 499

328. Joule's experiment. Determination of the mechanical equivalent of

heat 506

329. Attraction of iron filings by a natural or artificial magnet 512

330. Magnetic pendulum 513

331. Attraction of a magnetic bar by iron 514

332. Magnetic figures. Distribution of iron filings on a surface . . . . 515

333. Consequent points, or secondary poles of magnets 515

334. Attraction and repulsion of the poles of magnets 516

335. Magnetization by the influence of magnetism 517

336. Magnetization by influence at a distance 518

337. Rupture of a magnet ; disposition of the poles in the pieces . . . . 518

338. Magnetic needle 519

339. Magnetic declination at Paris, October 1864 520

340. Inclination of the needle at Paris, October 1864 520

341. Magnetic needle, showing both the inclination and declination . . . 521

342. Coulomb's magnetic balance 522

343. Processes of magnetization. Method of single touch 523

344. Magnetism by separate double touch. Duhamel's process 524

345. Magnetization by the method of ^pinus 525

346. Compound magnet, formed of twelve magnetic bars 526

347. Iron horse-shoe magnet, with its armature and keeper 527

348. Magnet formed of two compound bar magnets 527

349. Natural magnet furnished with its armature 528

350. Attraction of light bodies 533

351. Electrical pendulum. Phenomena of attraction and repulsion . . . 535

352. Distribution of electricity on the surface of conducting bodies . . . 539

353. Distribution of electricity on the surface of bodies 540

354. Faraday's experiment to prove that electricity is located on the outer

surface of electrified bodies 541

355. Tension of electricity at the different points of a sphere and of an

ellipsoid 542

356. Tension of electricity on a flat disc, and on a cylinder terminated by

hemispheres . 542

357. Power of points. Electric wind 544

358. Electric fly 544

359. Electricity developed by influence or induction 545

360. Distribution of electricity on an insulated conductor electrified by

induction 546

361. Electrical induction through a series of conductors 548

362. Cause of attraction of light bodies 549

363. Quadrant electroscope 551

364. Gold-leaf electroscope 551

365. Otto von Guericke's electric machine 553

366. Plate electric machine . 555

xxxii LIST OF ILLUSTRATIONS.

FIG. PAGE

367. Nairne's machine, furnishing the two electricities 558

368. Armstrong's hydro-electric machine 560

369. Electrophorus with resin cake 561

370. Electrical bells . . . . 562

371. Electrical hail 563

372. Luminous tube ; 564

373. Luminous globe . 565

374. Luminous square 565

375. Kinnersley's thermometer 566

376. Electrical mortar • ,- . ' < • •. . . 566

377. Cuneus' experiment (the Leydea jar) 268

378. Charging the Leyden jar 569

379. The condenser of ^Epinus 570

380. Charging the condenser of .^pinus 571

381. Leyden jar with moveable coatings 572

382. Instantaneous discharge of a Leyden jar by means of the discharger . 573

383. Successive discharges of a Leyden jar. Chimes 574

384. Sparkling Leyden jar 574

385. Leichtenberg's figures. Distribution of the two kinds of electricity . 575

386. Leichtenberg's figures. Distribution of the positive electricity . . . 576

387. Leichtenberg's figures. Distribution of the negative electricity . . . 577

388. Battery of electrical jars 578

389. Universal discharger 579

390. Experiment of perforating a card 580

391. Experiment of perforating glass 581

392. Franklin's portrait experiment . 582

393. Press used in Franklin's portrait experiment 582

394. Volta's pistol. Interior view 583

395. Explosion of Volta's pistol 583

396. Fulminating pane 584

397. Contraction of the muscles of a frog. Repetition of Galvani's experiment 586

398. Volta's condenser 588

399. Voltaic or column pile 589 •

400. Electricity developed by chemical action 591

401. Crown, or cup pile 593

402. Wollaston's pile 594

403. Spiral pile 595

404. Couple of Daniell's battery 596

405. Couple of Bunsen's battery 597

406. Pile formed by five Bunsen's elements 598

407. Decomposition of water by the voltaic pile 601

408. Action of an electrical current on the magnetic needle 605

409. Deviation of the southern pole towards the left, under the influence of

the upper current 606

410. Deviation to the left of the current. Lower current 606

411. Deviation to the left of the current. Vertical current 607

41 2. Schweigger's multiplier 607

413. Concurrent actions of the different portions of the wire in the multiplier 608

LIST OF ILLUSTRATIONS. xxxiii

FIO. PAGE

414. System of two astatic needles . 609

415. Galvanometer . . 609

416. Action of a magnet on a current 611

417. Law of the attraction and repulsion of a current by a current . . . 611

418. Direction of a solenoid in the meridian, under the action of the earth . 613

419. Particular currents of magnets 614

420. Resulting currents at the surface of a magnet 614

421. Magnetization of a steel needle by a solenoid : right handed and left

handed spirals 615

422. Magnetization by a spiral : production of consequent points .... 616

423. Horse-shoe electro-magnet 617

424. Electro-magnet .* 617

425. Electro-magnet with its charge 617

426. Magnetic chain 618

427. Induction by a current 621

428. Induction by the approach of a current 622

429. Induction by a magnet 623

430. Induction by the approach or removal of a magnetic pole 624

431. Clarke's magneto-electric machine 625

432. RuhmkorfFs induction coil 627

433. Commutator of RuhmkorfFs machine. Plan and elevation .... 629

434. Sparks obtained by the discharge of static electricity 632

435. Forms of electric discharges (Van Marum) 633

436. Electrical brush, according to Van Marum 635

437. Positive and negative brushes 636

438. Light in the barometric vacuum 636

439. The electric egg 637

440. Electric light in rarefied air. Purple bands 637

441. Carbon points of the electric light, and the Voltaic arc between them . 639

442. Luminous sheaf in rarefied air. Discharge of induction currents . . 641

443. Stratified light in rarefied gas 641

444. The mirage in the African desert 647

445. Explanation of a mirage 649

446. Paths of the effective rays through a drop of rain after a single internal

reflection 651

447. Path of the effective rays after two interior reflections 651

448. Theory of the rainbow ; formation of the principal and secondary arc . 653

449. De Saussure's hair hygrometer 656

450. Forms of snow crystals (Scoresby) 657

451. Dissection of a block of ice by the solar rays. Crystalline structure

of ice 660

452. Ice-flowers (Tyndall) 661

453. Rutherford's maximum and minimum thermometers 662

454. Maximum and minimum thermometers of M. Walferdin 663

455. The Gramme machine 679

456. Brayton's petroleum motor . 680

INTEODUCTOEY CHAPTER

FRENCH AND ENGLISH SCIENTIFIC UNITS.

IN the varied examinations into the qualities and properties of
matter with which Physical Science is especially concerned,
certain units of measurement are essential. And it is unfortunate
that in different countries these units are not the same. The Metric
or French system, however, is now so universally acknowledged to
be the best for scientific purposes, that the Editor by the advice of
eminent scientific friends has retained it in this work. Its retention
renders necessary a few words by way of introduction.

One great advantage of the Metric System over our own is that it
is a decimal system : thus, by the simplest decimal system of multi-
plication and division, we are enabled to perform with speed and
ease any calculations connected with it which may be necessary;
another is that the same prefixes are used for measures of length,
surface, capacity, and weight ; and, finally, these various measures are
related to each other in the simplest manner.

Unit of Length. — The English unit of length is the yard, the length
of which has been determined by means of a pendulum, vibrating
seconds in the latitude of London, in a vacuum, and at the level of
the sea. The length of such a pendulum* is to be divided into
3,913,929 parts, and 3,600,000 of these parts are to constitute a yard-
The yard is divided into 36 inches, so that the length of the seconds
pendulum in London is 39*13929 inches.

The French unit of length, called the mbtre (from fierpea), I measure),
has been taken as being the ten-millionth part of the quadrant of a

xxxvi

INTRODUCTORY CHAPTER.

meridian passing through Paris ; that is to say, the ten-millionth part
of the distance between the equator and the pole, measured through
Paris. It is equal to 393707898 inches. The metre is divided
into one thousand millimetres, one hundred centimetres, and
ten dddmktres ; while a decametre is ten metres, a hectometre one
hundred metres, a kilometre one thousand metres, and a myriometre,
ten thousand metres. The following table gives the value of these
measurements in English inches and yards : —

In English Inches.

In Englifch yards.

Millimetre

0-03937

0-0010936

Centimetre
Decimetre . ....

0-39371
3-93708

0-0109363
0-1093633

METRE

39-37079

1-0936331

Decametre

393-70790

10-9363310

Hectometre
Kilometre .......

3937-07900
39370-79000

109-3633100
1093-6331000

Mvriometre

393707*90000

10936-3310 00

One English yard is equal to O91438 metre ; while one mile is equal
to 1-60931 kilometre.

In the annexed woodcut a decimetre, with its divisions into
centimetres and millimetres, is shown, and compared with four inches
divided into eighths and tenths.

Unit of Surface. — For the unit of surface, the square inch, foot,
and yard adopted in this country are replaced in the metric system
by the square millimetre, centimetre, decimetre, and metre.

1 square metre
1 square inch
1 square foot
1 square yard

1-1960333 square yards.
6-4513669 square centimetres.
9-2899683 square decimetres.
0-83609715 square metre.

INTRODUCTORY CHAPTER.

xxxvii

In the annexed woodcut a square inch and a square centimetre
are shown, in order to give an idea
of measures of surface which will
often be referred to in the following
pages.

Unit of Capacity. — The cubic inch,
foot, and yard- furnish measures of
capacity ; but irregular measures, such

as the pint and gallon, are also used in this country. The gallon
contains ten pounds avoirdupois weight of distilled water at 62° F. ;
the pint is one-eighth part of a gallon. The French unit of capacity
is the cubic decimetre or litre (\irpa, the name of a Greek standard
of quantity), equal to 1/7607 English pints, or O2200 English gallon ;
and we have cubic inches, decimetres, centimetres, and millimetres.

1 litre 61-027052 cubic inches.

1 cubic foot 28-315311 litres.

1 cubic inch 16'386175 cubic centimetres.

1 gallon 4-543457 litres.

Unit of Mass or Weight. — The English unit of weight— the
pound — is derived from the standard gallon, which contains 277'274
cubic inches ; the weight of one-tenth of this is the pound avoirdu-
pois, which is divided into 7,000 grains. The French measures of
weight are derived at once from the measures of capacity, by taking
the weight of cubic millimetres, centimetres, decimetres, or metres of
water at its maximum density, that is at 4° C. A cubic metre of
water is a tonne, a cubic decimetre a kilogramme, a cubic centimetre
a gramme, and a cubic millimetre a milligramme.

.' ••'

In English grains.

In Ib. Avoirdupois. ,
1 lb.=700 grammes.

Milligramme (T y^th part of a 'gramme)
Centigramme ( TJffth „ „ )
Decigramme ( ^th „ „ )
GRAMME

0-015432
0-154323
1-543235
15-432349

0-0000022
0-0000220
0-0002205
0-0022046

Decagramme ( 10 grammes) . . .
Hectogramme ( 100 „ ) . . .
: Kilogramme ( 1000 ,, ) . . .
Myriogramme (10000 „ ) . . .

154-323488
1543-234880
15432-348800
154323-488000

0-0220462
0-2204621
2-2046213
22-0462126

xxxviii INTRODUCTORY CHAPTER.

Besides these units, there are others on which a few words
may be said, as the units before referred to are implicated. The
Unit of Time or Duration is the same for all civilised coun-
tries. The twenty-fourth part of a mean solar day is called
an hour, and this contains sixty minutes, each of which is divided
into sixty seconds. The second is universally used as the unit
of duration.

Having now units of space and time, we are in a position to fix
upon a Unit of Velocity. — The units of velocity adopted by different
scientific writers vary somewhat ; the most usual, perhaps, in regard
to sound, falling bodies, projectiles, &c., is the velocity of feet or
metres per second. In the case of light and electricity, miles or kilo-
metres per second are employed.

We have next the Unit of Mechanical Work. — In this country the
unit of mechanical work is usually the foot-pound, viz. the force
necessary to raise one pound weight one foot above the earth in
opposition to the force of gravity. A horse-power is equal to 33,000 Ib.
raised to a height of one foot in one minute of time. In France the
kilogrammetre is the unit of work, and is the force necessary to
raise one kilogramme to a height of one metre against the force of
gravity. One kilogrammetre— 7'233 foot-pounds. The cheval vapeur
is nearly equal to the English horse-power, and is equivalent to
32,500 Ib. raised to a height of one foot in one minute of time.
The force competent to produce a velocity of one metre in one
second, in a mass of one gramme, is sometimes adopted as a unit
of force.

Unit of Heat. — These units vary : the French unit of heat, called
a calorie, is the amount of heat necessary to raise one kilogramme
(2-2046215 Ib.) of water one degree Centigrade in temperature ;
strictly from 0° C. to 1° C. In this country we sometimes take one
pound of water and 1° Fahrenheit as the units ; sometimes one pound
of water and 1° C.

Thermometric degrees. — The value of different thermometric

INTRODUCTORY CHAPTER.

XXXIX

degrees is discussed in the work itself (vide Heat, Book IV.,
Chapter i.). The following facts may be found useful : —

1° Fahrenheit
1° Centigrade
1° Reaumur

= 0-55° C. = 0-44° R.
= 0-80° R. = 1-81T F.
= 1-25° C = 2-25° F.

Centigrade degrees

-T- 5

9 +

Reaumur ,,

-f- 4

9 +

Fahrenheit „

- 32

~^-

9 X

)> 1?

- 32

-f-

9 X

Centigrade „

-4- 5

Reaumur „

— 4

Fahrenheit degrees.

» >»

Centigrade „
Reaumur „

>i jj

Centigrade r

BOOK I.

GEAVITY.

OF THE

UNIVERSITY

PHYSICAL PHENOMENA.

BOOK I.
GRA VI TY.

CHAPTER I.

PHENOMENA OF GRAVITY ON THE SURFACE OF THE EARTH.

A STONE left to itself in the air falls, and its movement is
arrested only on touching the ground ; a round body, or
a solid ball, rolls along a plane inclined , to the horizon ; a liquid
mass, such as a brook or large river, flows on the sloping sur-
face which forms its bed; smoke and steam rise into the air. All
these phenomena, and many others that we shall review, are the
varied manifestations of one ever-active force, universally distributed
throughout all nature, which is called Weight.

All bodies, without exception, which are found on the surface
of our planet — in the depths of its crust, or in the gaseous strata
of which its atmosphere is formed — have weight. This is a fact so
obvious that in the case of solid and liquid bodies it hardly requires
to be stated. We shall soon have occasion to show that it holds
good also with regard to gases and vapours.

B 2

PHYSICAL PHENOMENA.

[BOOK

Nor is it only moving phenomena which familiarize us with
the action of weight: it exercises itself also incessantly on bodies
which appear to us to be at rest, and which in reality are only in
equilibrium. The stone which has touched the
ground, the fall of which our eyes have followed,
continues thenceforth to weigh on the surface
which upholds it, and this pressure, which is
rendered evident by the constant tension of a
spring (Fig. 1), is rendered sensitive to our
organs by the effort which the hand is obliged
to use to support the stone.

A book placed on the table remains at rest
but presses on its support, which itself rests on
the ground. A mass of metal suspended at
the lower end of the thread or flexible cord
stretches the thread or cord ; this tension, which
continues as long as the suspending thread is
not cut, proves the continuous action of the
force on the suspended body.

•IP ct We must therefore clearly understand that

rest is not synonymous with inaction, and we
may be assured that, on the earth, no material
particle, whether solid, liquid, or gaseous, is
ever for one moment free from the action of this force.

Let us now endeavour to give a general picture of the terrestrial
phenomena — phenomena of equilibrium and of motion — which are
produced by this force.

Astronomy teaches us that the earth is of the form of a nearly
spherical ball, and has two movements — movements in which all
the parts of its mass participate at the same time : one of uniform
rotation round one of its diameters, the other of translation, which
draws it with varying velocity along an elliptic orbit, the sun
being in a focus of that orbit. But neither the one nor the
other of these movements directly affects the equilibrium of its
various parts. The solid masses which form its crust ; the nucleus,
probably in a state of incandescent fusion, which forms the interior ;
the liquid part of its surface, the oceans; and lastly, the gaseous
envelope which surrounds every portion of the spheroid, are in a

FIG. 1.— Action of weight
shown by the tension of
a spring.

CHAP, i.] PHENOMENA OF GRAVITY. 5

state of relative stability, resulting from mutual pressure, due to
the force which is now in question.

It appears certain that the entire earth was once fluid, and that
the different strata of which its interior is formed have ranged
themselves in the order of their densities — that is to say, the
heaviest at the centre, the lightest at the surface, according to the
same conditions which experience has proved to be necessary to
the stability of liquids and to their equilibrium under the action of
weight. And — to speak only of the parts accessible to observation
— it is seen that such is precisely the order of their succession.
Below we have the solid crust— the solid surface of the earth :
afterwards comes, spread over three quarters of this surface, the
liquid part or sea ; then above both, the gaseous strata which form
the atmosphere. Of these different constituents, the air presses on
the water, and both press on the solid ground.

Let us examine the surface of the continents and islands. We
find everywhere that the relief of the ground is such that all its
parts mutually support each other. In the mountains, as in the
plains, weight acting on each particle has arranged the masses in
such a way that equilibrium is never or very rarely destroyed.
Suppose the action of weight suppressed ; the other physical forces,
no longer finding resistance, would overturn the fields, rocks, and
mountains, and would everywhere substitute disorder and confusion
in place of the order which results from their present stability.
It is again the pressure due to weight which man utilizes when
he builds his most durable constructions in imitation of nature.
The mass of the materials, their vertical disposition, or, better still,
their slope, as in the case of the Pyramids of Egypt, have enabled
some of the monuments constructed by man to defy the action of
the elements and of centuries. We shall have occasion to notice
in the second part of this work other applications of the action of
weight to the arts and various industries. Let us here only remark,
as an instance of this, that we look to it to produce adherence of
the smooth wheels of locomotives to the rails : it is the enormous
weight of the engines which prevents their driving-wheels from
continually revolving without making any progress ; and it is not
a little curious that, in the infancy of the locomotive, the result of
the pressure on the rail due to the weight of the engine was so

PHYSICAL PHENOMENA. [BOOK r.

little understood, that it was thought that cogged wheels instead of
smooth ones would be necessary.

It is their weight also which keeps the waters of rivers in their
natural beds, and lakes and seas in their basins, where these masses
would remain at rest if exterior forces did not perpetually arise
to agitate them. It happens sometimes that, under the influence
of causes of irregular and terrestrial origin, — such as earthquakes
and winds, to which may be added the periodical oscillations of the
tides, — the sea is upheaved to great heights, and breaks beyond
its usual limits. But it is soon drawn back to its more common
state of equilibrium, either by its own weight or by friction —
another cause of stability, the origin of which is also weight.
Laplace, as the result of an inquiry into what were the conditions
necessary to the absolute stability of the equilibrium of seas, proved
that it is sufficient that the density of the ocean be less than that
of the earth — a condition which is precisely realized in nature.
Thus, if they were lighter, the waters of the sea would be in a
perpetual state of mobility; if they were heavier, the variations
from a state of equilibrium owing to accidental causes would be
considerable, and would occasion frightful catastrophes both on
continents and islands.

But the persistence of the action of weight is not observable
only in the land and water masses: the air is also subject to it.
Without this pressure, which keeps them to the earth's surface,
the elasticity, or the force of expansion, which is, as we shall soon
see, a distinctive property of gases, joined to the centrifugal force
due to the rotation of the earth, would soon dissipate the atmo-
sphere into space.

Such are, as a whole, the phenomena due to the continuous and
latent action, so to speak, of weight on our globe. It is this action
which everywhere maintains equilibrium, and which re-establishes
it when it is disturbed by the action of physical forces.

The phenomena of motion, due to the same force, form an
equally interesting and magnificent picture. The infiltration of the
waters through the earth's surface to different depths is due to this
irresistible tendency of all bodies towards the centre of the earth.
It is this tendency which by degrees undermines the land and rocks,

CHAP. I.] PHENOMENA OF GRAVITY.

and, disturbing their equilibrium, gives rise to the falling away of
the sides of mountains and hills, and in time fills up the valleys.
These movements have not the action of weight only for their origin,
and we shall see further on how this action combines itself with
those of other physical or chemical forces, and particularly with that
of heat, to cause most of the motion -of which the surface of our
globe and its atmosphere are the constant scene.

Often the work of disorganization remains unperceived until the
instant when the catastrophe occurs. Masses of high rocks being
undermined, all at once lose their equilibrium, and slide or are
dashed down, destroying everything in their path. Entire mountains
have thus covered towns and villages with their debris, and history
has recorded numerous examples of these terrible events. In the
thirteenth century, Mount Grenier, the summit of which still towers
above the mountains which border the Valley of Chambery on the
south, partly crumbled away, and buried the little town of Saint-
Andre' and many villages: the " dbimes de Myans" are still shown,
where lie the debris and the victims. In 1806 a no less terrible
landslip took place, and precipitated from the sides of Mount
Euffi, into the Valley of Goldau, an enormous mass of rock, which
completely buried many villages, and partly filled up a little
neighbouring lake.

It would be superfluous to calculate what is the destructive
energy of similar masses precipitated by the action of weight from
a height often prodigious, and the velocity of which increases with
the height of the fall. Avalanches are phenomena of the same
order, and are more frequent than the fall of mountain-sides and
rocks. Masses of snow, collected on the inclined side of a mountain,
or on the edge of a precipice, slide by their own weight, then detach
themselves, and fall, crushing everything in their path. Often a slight
shock — a pistol-shot, or a shout even — is sufficient to destroy the
equilibrium, and occasion the phenomenon. In the icebergs, or
mountains of ice in the polar regions, the pressure of the blocks
one upon the other gives rise to similar effects, in which the irre-
sistible action of weight again shows its power. Glaciers, too — those
rivers of hardened snow pressed into compact ice — descend the slopes
of the mountains under the pressure of the weight of the upper
strata. This movement of slow progression is so irresistible, that

8 PHYSICAL PHENOMENA. [BOOK i.

the lateral and underlying rocks are striated and polished by the
crystalline mass, and by the debris of boulders and pebbles which
it draws along.

In volcanic eruptions, the explosive force of the interior gases
often sends forth into the air cinders, fragments of stone, and rocks.
But if these masses thus seem to escape for a moment from the
action of gravity, the strife of the two forces is not of long duration,
and the projectiles obey the invincible law of all terrestrial bodies.
It is the same law which determines the fall of hail, rain, snow —
that is to say, the particles of aqueous vapour which have been
condensed, and thus rendered heavier than the stratum of the air
to which they rose, under the combined influence of heat and even
— paradoxical as it may seem — of weight itself.

Thus much, then, concerning the fall, properly so called, of
bodies of which the equilibrium, from some cause or other, has
been disturbed. But there is, on the surface of our planet, quite
another series of movements, in which weight plays the most im-
portant part, and the continuity of which produces an admirable
circulation on our planet, without which life itself would soon be
extinct.

The incessant evaporation of liquid masses gives rise to the
formation of clouds, and it is the difference between the weight
of the air, and of the particles of vapour of which clouds are
formed, which causes their ascending movement. Eain, due to the
fall of these same particles when liquefied, falls through the action of
terrestrial gravity, to the lowest levels — forms brooks and rivers, and
these fluvial masses following the natural slope of the ground, reach
the sea, sometimes flowing with majestic slowness, at other times
rushing noisily over a rugged bed. Sometimes stopped by natural
obstacles, the waters spread themselves in the form of lakes : or
else, arriving at the edge of a wall of rocks, flow over in cascades.
Such are the falls of the Rhine at Schaffhausen, of Niagara, and
the Zambesi cataracts in Central Africa.

Currents are not peculiar to the solid portion of the surface of
the earth. The ocean is furrowed with real rivers, the regular
movements of which are determined by the action of weight,
although their origin is due to another physical agent — heat. It is
also weight which regulates all the movements of the atmospheric

CHAP, i.] PHENOMENA OF GRAVITY.

gaseous mass, which unites its restless power to the action of the
other natural forces.

In conclusion, there is no action on our planet in which weight
does not intervene sometimes to establish equilibrium, at others to
give rise to motion. Even when it appears to be destroyed or
counterbalanced, it is still at work, and is ever present wherever a
particle is found, apparently invariable, and, according to the ideas
experiment has given us of matter, as indestructible and eternal as
matter itself.

10 PHYSICAL PHENOMENA. [BOOK i.

CHAPTER IT.

WEIGHT AND UNIVERSAL GRAVITATION.

ALL the varied and numerous phenomena to which we referred in
the previous chapter have the same origin — a fact which will
become more evident as experimental proofs are given. All are due
to the action of a similar cause, or force, since this term is now
given to every cause capable of producing or of modifying motion
in a body as of bringing it back to a state of rest.

What the essence or primordial cause of this force is, is a problem
which science does not seek to solve : it confines itself to studying
the effects of the force by means of observation, and thence to
discover the law which regulates them ; and in this we shall soon
see it has completely succeeded. The direction of the action . of
weight, that is to say, the line in which the heavy body tends to
move or is moved when it meets with no resistance ; the point at
which the force is applied ; and, lastly, its intensity or the energy
with which it attracts or pulls each material particle, are facts
exactly determined. We shall recur in detail to them in the
following chapters.

We know by experiment that a force resides somewhere, that it
has its centre of action in a given place. We may say more : we
cannot conceive it acting without a material body to act upon.
Where, then, is the centre of action of terrestrial gravity ? It is
not in the heavy body itself. Indeed, according to a principle of

CHAP. IF.] WEIGHT AND UNIVERSAL GEAVITATION. 11

paramount importance in the science of motion, or dynamics — the
principle of inertia — a body cannot put itself in motion when it is
at rest, nor of itself modify its movement when in motion.

It is, then, outside a falling body that we must look for the cause
of its fall. We are so accustomed, from our infancy, to see all
bodies which surround us falling under the action of weight, or in
other words to see the force of gravity at work, that the question
seems to be an idle one. But, as D'Alembert has said, " It is not
without reason that philosophers are astonished to see a stone fall,
and those who laugh at their astonishment would soon share it
themselves, if they would reflect on the question."

It is from above downwards, in the vertical of any place — that
is to say, in a line upright or perpendicular with regard to the surface
— that all bodies fall, and it is in the same direction that they press
on their supports. Weight, then, we see, acts as it were from the
interior of the earth ; and since for points at short distances apart,
the verticals, or upright lines, at these points seem parallel, it may
be supposed that, instead of a single force, there exists an infinity
of forces, all acting in the same manner and in the same direction.
But it is easily seen that this last conclusion is not exact.

Weight, or gravity, everywhere acts in the same manner. In
all places, in all latitudes, at
the equator, at the poles, in the
temperate regions of the world,
its influence is felt always
in a direction perpendicular to
the horizon. To know at what
point of our globe this multiple
action is concentrated, we must
find out if all the verticals have
a single common meeting-place.
Let us take any one of the
meridians of our planet. Each
part of the circle which forms

the meridian indicates an horizon. FIG. 2.- Convergence of the verticals towards the

centre of the earth.

and the line perpendicular to this,

or the vertical of the place, is no other than one of the radii of

the circumference ; that is to say, a line running to the centre of the

12 PHYSICAL PHENOMENA. [BOOK i.

sphere. Thus all verticals, such as A z, Fig. 2, though apparently
parallel when adjacent ones only are considered, are in reality con-
vergent ; they are directed towards the centre, c, of the earth. This
is only a first approximation : the earth not being exactly spherical,
but flattened at the poles and swelled out all round its equatorial
circumference, the verticals of the different latitudes do not pre-
cisely tend to the same point. We shall observe also that besides
this cause of deviation there exist local irregularities which render
the determination of the real centre of the action of gravity very
complex. But from our present point of view these different
deviations have no importance. Let us now register this first
fundamental result :

All bodies have a tendency to fall towards the centre of the earth.
Gravity acts on them, as a single force concentrated in this point.

This law has no exception. It applies to bodies placed on the
surface or at any height whatever in the atmosphere ; on the earth's
crust, or in the deepest mines, observation always confirms its truth.

This convergence of all falling bodies which tend towards one
point, is in contradiction with a popular prejudice still prevalent.
Many persons when they are told that the earth is round, and that
it is inhabited on every part of its surface, cannot conceive how at
their antipodes the inhabitants of the planet can walk, as it were,
feet uppermost, and how material bodies, solid or liquid, can remain
in equilibrium. By reflecting a little they would soon see that the
idea of above and below is quite relative; that on a sphere in space
each part of the surface is equally horizontal, and the tendency of all
bodies towards the centre of the sphere well explains the state of equi-
librium which exists on whatever part of the surface they are placed.

But whence comes this central force ? Is it a secret property
independent of matter ? Does the earth alone enjoy this mysterious
power ?

These important questions remained unanswered two centuries
ago, since which time Galileo's experiments on falling bodies,
and the profound speculations of Huyghens on the principles of
mechanics, enabled the genius of Newton to reach the general
cause which produces all the phenomena of gravity on the surface
of the earth as well as throughout the entire universe. Weight is,
in fact, a particular case of a force at work in all parts of the

CHAP, ii.] WEIGHT AND UNIVERSAL GRAVITATION. 13

universe — the force of universal gravitation. In virtue of this force
any two particles of matter gravitate or fall towards each other, that
is to say, they have a mutual tendency to re-unite, which depends
on their respective masses and on their distance apart. Here is the
law of this dependence : —

If we take for unity the force which draws two equal masses,
situated at a unit of distance apart, towards each other, if one of
the masses be doubled, the force itself will be doubled : if the other
mass be replaced by one three times greater, the force will be
now tripled, and, in consequence, will be six times greater than
at the beginning.

If now, the masses remaining the same, we make the distance
twice, three times, four times less, the force of gravitation will be
four, nine, sixteen times greater.

Thus, attraction, or gravitation — we shall use this latter term in
preference (discarding altogether in future the term weight, which
by this time should have served its purpose), because it supposes
nothing as to the unknown essence of the force itself — is propor-
tional to the product of the masses, and varies inversely as the square l
of their distances.

Such is the fundamendal principle of which the phenomena of
weight are so many particular manifestations. It was not an easy
thing to deduce from it all the consequences, to calculate the re-
ciprocal actions of all the small masses composing the entire bulk
of the earth, and the effect resulting from all these combined actions.
Newton, and after him the great geometers who have developed his
discovery, D'Alembert, Euler, Maclaurin, Lagrange and Laplace, have
devoted themselves to this task. They have shown that a spherical
mass of homogeneous matter acts on an exterior point in the same
way as if all the matter were concentrated at its centre. The same
thing is true of a homogeneous spherical layer, and consequently of
a series of strata of this same form, the density of which continues
to increase according to a definite law.

Such is precisely the case with the earth: and Newton thus
explains how the direction of gravity is everywhere vertical to the

1 The square of a number is the product of the multiplication of the number by
itself: thus 9 is the square of 3 ; 100, the square of 10; 1,000,000 the square
of 1,000, and so on.

H PHYSICAL PHENOMENA. [BOOK i.

surface, or the straight line between the heavy body and the centre
of the globe.

A body situated in the interior of the earth is attracted by the
mass which lies beneath it, but the action of the particles of the
exterior layer destroy each other, so that the intensity of gravita-
tion goes on diminishing from the surface to the centre.1 In like
manner, this intensity diminishes in the case of bodies exterior to
the earth, in proportion as their distance from the earth increases.

Thus, then, the source of gravity at the surface of our globe lies
in the entire mass of which it is composed. There is not a single
particle, however small it may be, which does not take part in the
general action. Nay, more : when a stone falls, at the same time
that it feels the influence of the mass of the globe it reacts on this
globe by its own bulk : the two bodies come together by gravitating
one towards the other. The motion of the stone, however, is alone
perceptible, as its mass is almost nothing compared to that of the
earth. But more of this presently.

It has been stated that gravitation is universal. Not only, indeed,
does it govern all the phenomena of terrestrial gravity, but it extends
its power to the most remote parts of the heavens. The moon
and the ea-rth gravitate reciprocally towards each other, arid they
both gravitate towards the sun. All the planets of our solar system
continually act on one another, and on the immense sphere which
shines at their common focus. By its enormous mass, the sun
keeps all of them in their orbits, so that the movements of all the
celestial bodies which compose the system are mutually balanced
and varied under the influence of the same force perpetually acting
in each of them.

We have endeavoured to give elsewhere 2 an idea of these grand
problems, the solution of which is the triumph of science. Let us

1 In fact, the intensity of gravity first increases from the surface to a distance
from the centre which is estimated at nearly seven-tenths of the radius ; it after-
wards lessens to the centre. These variations are due to this fact, that the con-
centric layers of which our globe is formed are not homogeneous ; their density
increases from the surface to the centre, and the density of the superficial strata is
less than two-thirds of the mean density. These results have been deduced from
pendulum observations.

2 " The Heavens : an Illustrated Handbook of Popular Astronomy." By
A. Guillemin. Translated by Mrs. Lockyer.

CHAP, n.] WEIGHT AND UNIVERSAL GRAVITATION. 15

recall only two proofs of the existence of the force of universal
gravitation in the celestial spaces. The tides — those periodical
oscillations of the sea — are produced by the action of the masses
of the moon and sun : and aerolites, celestial bodies in miniature,
which sometimes fall on our planet, show that the action of terrestrial
gravity is capable of diverting exterior masses from their orbits.

The most recent researches in stellar astronomy prove, moreover,
that the same force regulates the movements of the most distant
stars. The double stars are systems of suns, situated at immense
distances from our globe, and revolving round each other: here,
again, it is certain that their motions are effected according to the
same laws which regulate those of the planets — laws which are
a direct consequence of gravitation, that is, of their weight.

16 PHYSICAL PHENOMENA. [BOOK i.

CHAPTEK III.

LAWS OF ATTRACTION. — FALLING BODIES.

First experiments of Galileo on falling bodies — E^ual velocity of bodies falling
in vacua — Vertical direction of gravity — Deviation from the vertical due.
to the rotation of the earth — Galileo's inclined plane ; Attwood's machine ;
Morin's machine ; kvvs of falling bodies — Influence of the resistance of the
air on the velocity of bodies falling through the atmosphere ; experiments of
De"saguliers.

IT is recorded of Galileo that in his youth, when he was Professor
of Mathematics at the University of Pisa, making his first
experiments on the fall of heavy bodies, he wished to see if it were
true, as had been said and believed from the time of Aristotle, that
the unequal velocity noticed in different bodies falling from a given
height was due to their unequal weight, or if it depended on the
nature of their material.

It was from the top of the famous Leaning Tower of Pisa that
he made these experiments : balls of different metals — gold, copper,
lead — having the same dimensions, but different weights, reached
the ground at nearly the same instant: a ball of wax, however
was much more retarded.

But the differences in the times of falling were not decided
enough to be attributed to the inequality of weight, so that it
did not appear probable that, as held by many, a thing twice as
heavy as another would fall twice as fast.

Having let the same thing fall through the air and through water,
he proved that the differences between the times of their respective
falls depended upon the density of the medium through which they
fell, and not on the weights of the falling bodies themselves.
Galileo hence concluded that it is to the resistance of the air we
must attribute the differences in the time of fall observed.

Fm. 8.— The Leaning Tower of Pisa.

CHAP. III.]

LAWS OF ATTRACTION.

When a body falls through air, or any other medium, it must
constantly displace the molecules of which the medium is composed,
and this is only possible by communicating to them a part of its
own movement. Suppose, then, we let fall at the same instant a
ball of lead and a ball of cork of equal weight : the latter loses
more of its own movement than the first does in displacing the
same quantity of air, because being of a lighter
substance it is larger, so that its speed is naturally
more diminished. The difference would be still
more perceptible if the fall, instead of being
effected through the air, were to take place in a
dense gas.

Galileo's discovery has since been exactly con-
firmed by experiment, and the honour of this
confirmation belongs to Newton.

Take a long glass tube furnished at both ends
with two frames of copper, one hermetically closed,
the other terminated by a stopcock, which allows
the tube to be adjusted on the table of an air-pump,
an instrument by which we can carry off, or exhaust,
the air which it contains. We now introduce into
one end of the tube bodies of different densities,
such as small pieces of wood, metal, feathers, paper,
cork, &c. After exhausting the air by means of
the air-pump, and turning the stopcock to prevent
its re- entrance, we turn the tube quickly, and place
it in a vertical position. All the little bodies at
once quit the top and fall together in the direction
of the axis of the cylinder (Fig. 4). If the tube be
inverted before the air is extracted, the unequal
rate of fall is clearly shown. If the experiment
be repeated several times, gradually letting the air
into the tube, it will be observed that this in-
equality decreases with the rarefaction of the air
in the tube. When the vacuum is as complete as
possible, all the bodies, although of different den-
sities, reach the lower part of the instrument at the same time.
It is then the resistance of the medium which is the cause of the

c 2

IG. 4. — Experiment
showing the equal ve-
locity of bodies falling
iTi vacuo.

20 PHYSICAL PHENOMENA. [BOOK T.

unequal rate of fall of bodies more or less heavy or more or less dense.
This resistance not only retards the motion, but also produces devia-
tions in the direction of the fall of the lighter bodies. A sheet of
paper, for instance, thrown into the air, takes a curved and often
very irregular flight to the ground. If we take a piece of money,
a penny for instance, and a disc of paper of the same size, and let
them fall separately from the same height, the money will touch
the ground before the paper. If we afterwards place the disc on
the penny, and let them fall together, both will touch the ground
at the same instant. The metal, in the latter case, prevents the
resistance of the air at the lower face of the paper.

What has just been said of solid bodies applies equally to liquids
and gases. A mass of water is divided, in its fall, into a number
of very small drops, the formation of which is due to the resistance of
the air and the mobility of the liquid particles. This division is very
perceptible in jets and in cascades or natural sheets of water which
fall from great heights. If, in order to experiment on the fall of
liquid bodies, we use a tube in which a vacuum has been made, the
water will be found to fall en Hoc to the lower part, keeping the
cylindrical form of the vessel, and its fall produces a dry noise —
a " click," as would that of a solid body. Such a tube forms what
is called a " water hammer." Smoke inclosed in a similar vacuous
tube also falls : it is thus seen that gaseous and vaporous bodies
have a certain weight.

We may state, in passing, that the resistance of the air to the
fall of bodies is a fortunate thing for agriculture, which already
suffers too much from the ravages produced by hail. Without this
resistance the smallest rain would strike the surface of the ground
with ever-increasing force, and would cause great damage.

Here, then, is one point gained, and the first law of falling
bodies proved : — All bodies situated on the surface of the earth,
whatever may be- their volume and their mass, fall in vacuo with
equal velocity.

An important inference may be at once drawn from this, namely,
that the force of gravity acts with equal energy on each particle
of matter, absolutely as if each of the particles which compose a
body were separate and independent. Experiment has proved to
us that gravity acts in the same way on all bodies, whatever be

CHAP. III.]

LAWS OF ATTRACTION.

their volumes and densities, whilst the weight of the body is the sum
of the action of gravity on all the particles, and in consequence
it varies, either with the volume, for homogeneous bodies of the
same kind of matter, or, if the volume changes, it varies with the
density.

Let us inquire further into the phenomena of the fall of bodies
on the earth's surface.

The direction of gravity — and this is a fact that every one can

Fin. 5. — The direction of gravity is perpendicular to the surface of liquids at rest.

prove for himself — is, in every part of the earth, vertical ; that is,
in a straight line perpendicular to the plane of the horizon.
This plane may be determined by the surface of still water. A
very simple practical way to assure oneself of this fact is to observe
the position that a flexible thread stretched by a heavy weight takes
when the thread comes to rest, after many oscillations. Such a

22 PHYSICAL PHENOMENA. [BOOK i.

thread is called a plumb-lime or plummet, and is used by work-
men who wish to construct an upright building. Placing the
plumb-line above a liquid mass at rest, for example a mercury
bath, it is easily seen that the direction of the string and that of its
image are in the same straight line (Fig. 5), and consequently, in
virtue of the laws of the reflection of light, which we shall discuss
in the sequel, both are perpendicular to the horizontal surface of
the liquid.

The different verticals, we have already said, are not parallel ; but
at very slight distances the angle which they form is so small that
it is impossible to measure it. This is not the case if we take two
places on the earth somewhat distant from each other : in this case
their respective verticals can be measured by means of astronomical
observations. If the two places are on the same meridian, and
have the same geographical longitude, the angle of the verticals
is measured by the difference of latitude. The difference between
the directions of gravity between Paris and Dunkirk is thus found
to be about 2° 12', between London and Edinburgh about 4° 25' ; the
vertical which passes through the top of the cross of St. Paul's
and that which passes through the flagstaff on Victoria Tower
make but a very small angle with each other.1

Hence it follows that the waters of a lake or of a sea are
bounded by a surface which is not plane, but spherical, or rather
spheroidal, although at every part or point of the earth's surface
it is confounded with the plane of the horizon of the place.

We must therefore understand that when it is said that heavy
bodies fall in a constant direction, which is that of the vertical of
the place, this constancy implies only a parallelism of fall at places
very near together.

Lastly, let us add that the rotatory movement of the earth
produces a deviation in the fall of bodies. A body at a (Fig. 6),

1 If the experiment is made in the neighbourhood of a very high mountain, the
plumb-line is deflected from the vertical, under the influence of the attraction of
the mass of the mountain. This deviation, always very slight, was first measured
by Bouguer and Lacondamine, on the side of the Chimborazo. In 1774 Dr.
Maskelyne measured the attractive influence of Mount Schihallion, which he found
equal to about 12" ; that is. two plumb-lines, situated on either side of the mountain,
instead of forming between them the angle indicated by the difference of latitude of
the stations, formed one larger by 12 seconds.

CHAP. IIL] LAWS OF ATTRACTION. 23

situated at a certain height in the air, would fall at the foot of the
vertical at A, if the earth was immovable. But during the time of
its fall, the rotatory movement makes it describe an arc a of, larger
than the arc A A" described by the base of the vertical. Left to
itself, it retains its velocity of primitive impulsion, and ought to
fall at A" to the east of the lower point. Such is the deviation which
the theory indicates, and which being nothing at the poles, goes on
increasing towards the equator. Experiment confirms the reasoning :
in the atmosphere, however, it is difficult to succeed in the experi-
ment, on account of the disturbances in the air ; but it can be proved

FIG. 6. — Eastern deviation in the fall of bodies.

that a metallic ball A dropped at the mouth of a very deep mine,
falls at B', a little to the east of the foot B of the plumb-line which
marks the vertical. The deviation depends of course on the depth
of the mine : at the equator it is 33 millimetres for a well 100
metres deep. For a mine at Freiburg, in Saxony, M. Reich proved an
eastern deviation of 28 millimetres at a depth of 158*5 metres, theory
indicating 26'6 millimetres. It is evident, then, that we have here an
experimental proof of the earth's rotation.

Galileo, in his experiments on the fall of heavy bodies, did not
confine himself to destroying the popular fallacy, which was still
prevalent in his time, regarding the inequality of the velocity of fall
being attributable to the difference of weight or to the density of the
substances. He observed that the velocity acquired increased with
the heights of the fall ; that the spaces traversed were not simply pro-
portional to the times employed to traverse them, — in fact, that the
fall of heavy bodies, instead of being a uniform, is an accelerated
movement. Such an assertion doubtless had been made before him,

24 PHYSICAL PHENOMENA. [COOK i.

but he had the glory of discovering the precise law of variation of the
velocity acquired and the space described. Supposing that gravity,
whatever its essence might be, acted always with the same force,
he concluded that the velocity acquired ought to be proportional
to the time, and ke proved his hypothesis by a celebrated experiment
to which his name has remained attached. This was the inclined
plane of Galileo. The rapidity with which heavy bodies, metallic
balls for instance, travel in their fall does not easily allow of direct
observation. But Galileo knew that a heavy body left to itself on

a plane inclined to the horizon,
and subjected only to the action
of gravity, follows in its move-
ments the same laws as if it fell
vertically ; the friction of the

Fia. 7. -Movement of heavy bodies on an body On the plane and the re-
inclined plane.

sistance of the air during the

fall, in the two cases being disregarded. The force which draws
the body down the inclined plane is no other than gravity,
diminished in the ratio of the two lines A c and A B, which measure
its height and its length.

In the case represented in the figure the force of gravity is
reduced to little more than a quarter of its natural value.

The movement being considerably retarded by this arrangement,
Galileo could easily measure the spaces traversed during each
successive second.

But as the experiments of the inclined plane do not give results
of great precision, the laws of falling bodies are determined at
the present day by various instruments which are found in all
physical laboratories, and which will be here described. Already
in the seventeenth century, Eiccioli and Grimaldi assured themselves
of the exactness of Galileo's experiments, but they confined them-
selves to dropping a weight from the tops of towers of unequal
heights, and measuring the times of the fall by the oscillations
of the pendulum. In 1699 Father Sebastian invented a machine
for the same purpose. Lastly, an English physicist, Attwood^
constructed one which still bears his name: and in our time
General Morin has invented another, which registers directly the
results of the experiment.

CHAP. III.]

LAWS OF ATTRACTION.

The plan invented by Attwood to retard the movement of falling
bodies is this: a very fine silken thread is passed round a wheel
(Fig. 8), moving easily on friction rollers, the thread having at
its two extremities metallic cylinders of exactly the same weight.
In this state, the pulley, the line, and the weights remain
at rest, because the two equal weights produce equilibrium. If
an additional weight is placed on one of them, the system will
be put into motion: the two portions of the line will be moved

FIG 8 —Pulley of Attwood's machine.

in an opposite direction, each still, however, keeping its vertical
direction. But it will be at once seen that the speed of the fall
will be the more retarded as the additional weight is small com-
pared with the sum of the two equal weights. Let us suppose
that each of these weighs 12 grammes, and the additional one
weighs 1 gramme only. The total weight of 25 grammes being
put into motion by a force which is only a twenty-fifth part, it is

PHYSICAL PHENOMENA.

[BOOK i.

clear that the speed will be that which

Km. 9.— Experimental study of the laws of falling bodies.
Attwood's machine.

a falling body would
possess if the inten-
sity of gravity were
twenty-five times less.
Observation is thus
rendered easy, with-

out disturbing
laws of motion.
9 shows

the

Fig.

arrangement of

the
the

machine. At the top
of a column a pulley
is seen, the axle of
which rests on two
systems of parallel
wheels (friction roll-
ers— see Fig. 8) ; then
the line which passes
round the pulley is
stretched by equal
weights on either side.
A vertical scale, care-
fully divided, is placed
behind one of the
weights, on which
scale the distance
from the base of the
weight to the zero of
the scale, that is, the
point of departure of
the weight, may be
read in each of its
positions.

This scale has two
movable plates, which
can be fixed by screws
at any of its divisions.

The lower plate simply arrests the movement of the system at will.

CHAP, in.]

LAWS OF ATTRACTION.

The other plate is in the form of a ring, and the opening is large

enough to allow the weight

suspended to the line p to

pass through, but on the other

hand stops the additional

weight p on account of its

O 1

elongated form. A pendulum
beating seconds is added :
each movement of the second-
hand makes a clear sharp
noise, by means of which
the passing seconds can be
counted without looking at
-the dial. A contrivance at-
tached to the clock enables
each experiment to begin at
the precise instant when the
seconds' hand is at the zero
of the dial, at the upper part
of the latter. The additional
weight, first placed above
the weight which occupies
the division 0 of the ver-
tical scale, is suddenly let
go by the action of the
mechanism, and motion
begins.

The experiments are per-
formed in this way : Place the
lower plate in such a place on
the column that the cylindri-
cal weight surmounted with
the weight p will touch it
precisely at the commence-
ment of the second second,
which is determined by the

coincidence of the second beat of the pendulum with the click of
the weight on the plate. Suppose this point be at the twelfth

FIG. 10. — Experimental study of falling bodies.
Law of spaces described.

28 PHYSICAL PHENOMENA. [BOOK i.

division at the scale (Fig. 10). It is then observed, in conducting
this operation successively during two, three, four seconds, &c.,
that the lower plate must be at the following divisions, in order
that the click of the weight coincides each time with the successive
beats of the clock. These divisions are marked by the numbers
48, 108, 192, &c.

Thus the spaces described are :—

After 1 second 12 centimetres.

„ 2 seconds 48 „ = 12 X 4

„ 3 „ v 108 „ =1-2X9

„ 4 „ ..... 192 „ = 12 X 16

„ 5 „ 300 „ = 12 X 25

The space, then, through which a falling body travels, must be
multiplied by the numbers 4, 9, 16, 25 .... to obtain the space
described during 2, 3, 4, 5 .... seconds of fall. If the additional
weight be changed, the numbers which measure the spaces traversed
in each second would change : their ratio, however, would still
remain the same.

Here, then, is the first law, the one discovered by Galileo :—

The .space described ly bodies falling freely under the action of
gravity is proportional to the square of the time elapsed from the
beginning of the fall.

It remains for us now to determine the law of velocity — that is,
to learn what is the speed acquired after 1, 2, 3 .... seconds of
fall. Whilst the body which falls remains subject to the action of
gravity, this velocity goes on increasing at each instant during the
fall, and cannot in consequence be directly observed. To render this
determination possible, the continuous action of gravity must be
suppressed at the moment the following second begins, so that the
body may continue to move uniformly, and in virtue of the acquired
velocity alone.

It is important to understand what is meant by the velocity of a
body which falls, or, to speak generally, which is endowed with an
accelerated motion. This velocity of motion at a given moment
is measured by the space through which the body would travel
uniformly in each of the following seconds if the force ceased to
act, and the motion ceased to be accelerated. The ring of Attwood's

CHAP. III.]

LAWS OF ATTRACTION.

machine realises this hypothesis. It is sufficient to fix it successively

at the divisions that were shown in the first experiment, then to

find by trial at which part of the

scale the lower plate must be in

order that the weight, relieved of

its overweight, may strike it at the

beginning of the following second.

The experiment, supposing that p
has the same mass as p', will give
the following numbers : 36, 96, 180,
&c. (see Fig. 11). Hence it follows
that the uniform velocity of falling
bodies, acquired after 1, 2, 3 . . . .
seconds of fall, is :

After 1 second .
„ 2 seconds.
3

24 centimetres per second.

48
72

The velocity goes on increasing in
proportion to the time; the second
law which governs the fall of heavy
bodies may then be thus enun-
ciated : —

When a heavy body falls freely
under the action of gravity, its spaed
is accelerated : its velocity, at any
moment of the fall, is proportional to
the time elapsed since the commence-
ment of motion.

It follows also from the same ex-
periments that the velocity acquired
after one second of fall carries the
body through double the space passed
through during the first second ; and
it is easily seen that this is indepen-
dent of the unit of time chosen.

The same laws are proved experimentally by means of the
machine invented by M. Morin, of which Fig. 12 gives a general
view. A weight of a cylindro-conical form descends freely along

FIG. 11. — Experimental study of fulling
bodies. Law of velocity.

PHYSICAL PHENOMENA.

[BOOK i.

two vertical rods: it is furnished with a pencil, which marks a
continuous line on a cylinder covered with a sheet of paper.

If the cylinder were immovable, the line marked by the weight
during its fall would be a straight vertical Line, which would indi-

FIQ. 12.— M. Morin's machine.

cate nothing as to the spaces traversed during successive seconds.
But the cylindrical column is made to turn uniformly on its axis,
by the aid of a system of toothed wheels moved by the descent of a
weight, and uniformity of rotation is produced by a fan -regulator,
the spindle of which is connected with the train. Owing to this
motion of the cylinder under the pencil in its descent, the pencil
traces a curve, and an examination of this curve shows us the law

CHAP. III.]

LAWS OF ATTRACTION.

which governs the spaces described by the body during each second
at different parts of its fall.

The curve is what is called in geometry a parabola, the funda-
mental property of which is as follows : — The distances of the
successive points of the curve from a line drawn perpendicular
to the axis of the parabola from its vertex, are proportional to
the squares of the distances of these points from the axis itself.
The line perpendicular to the axis being divided into five equal
parts, the five distances from the vertex to the points of division,

0, 1, 2, 3, 4, 5, will be in the ratio of Q

1, 2, 3, 4, 5, but the five vertical lines
let fall from the divisions will be in the
ratio of 1, 4, 9, 16, and 25, that is, propor-
tional to the squares of the first numbers.

Now the cylinder having turned uni-
formly on its axis, the equal portions of
the circumference which separate the
points of division of the horizontal line
mark the successive seconds of fall of the
weight, and the vertical lines are the spaces
traversed.

As to the law of velocities, it is a
direct consequence of that of spaces.

It must not be imagined that the

machines described give results of mathematical exactness. There are
many hindrances, such as the friction of the parts, and the resistance
of the air, which are opposed to such results ; but the differences
which arise from them are very slight.

•25

FIG. 13. — Parabola described by the
weight in its fall.

The experiments made by means of Attwood's machine show
moreover that gravity acts on the falling body in a continuous and
constant manner. For the spaces traversed during successive seconds
may be represented by the odd numbers 1, 3, 5, 7, 9, &c. ; and as the
velocities acquired at the commencement of the second and following
seconds are 2, 4, 6, 8, 10, &c., so that if no force acted during each
of these seconds, the spaces described would be represented by 2, 4,
6, 8, 10, &c., there is a constant difference, due to the continued
action of the force of gravity during each second, precisely equal to

32 PHYSICAL PHENOMENA. [BOOK i.

the space traversed during the first second. This difference therefore
marks the continuous action of gravity.

Again, it is seen that if a body is thrown up vertically, the
height to which it rises depends on the amount of force exerted, —
moreover, its velocity decreases, — and when it descends under the
action of gravity, its increasing speed at each point along its path
is precisely equal to that which it possessed at the same point
during its ascent.

The experiments made by the aid of Galileo's inclined plane
and Attwood's machine are founded on an artificial diminution of
the intensity of gravity, which, without changing the laws which
govern their fall, retards the motion of falling bodies. But precisely
on this account they do not enable us to measure the actual space
traversed during one second of fall ; and, moreover, the experiments
must be made in vaciw. M. Morin's machine would give this space
approximately, but the result would require corrections for friction
and the resistance of the air. We shall see further on that the
exact space has been determined by a more precise method.

The intensity of the force of gravity, moreover, as we shall soon
see, is not rigorously constant : it varies with the place, according to
latitude, and even with the local features of the terrestrial erust.
Lastly, in the same place, the intensity varies with the height
above the ground, or with the depth beneath it.

It must be borne in mind that the following figures refer to
the fall of bodies in vacua, in the latitude of London, and at a
little distance from the sea-level.

Under these conditions, a body travels during the first second
of its fall, 16^ feet. The velocity acquired after one second is
then 32J feet, and it is this latter number which is taken as a
measure of the force of gravity.

Fall in 1 second = 1 X 16,V - 16T\

„ 2 seconds = 4 X 16 ^ = 64^

„ 3. „ = 9 X 16& = 144ft

„ 4 „ = 16 X 16& = 257^-

„ 5 „ = 25 X 16,1 = 402^

The time that a body takes to fall from a certain height, and

CHAP, in.] LAWS OF ATTRACTION. 33

the velocity acquired at the moment it touches the ground, may
also be found in like manner.

In the case of a i ailing body the velocity is uniformly in-
creased by gravity ; in the case of an ascending one it is uniformly
decreased.

To throw a body to a vertical height of 400 feet we must give ft
a velocity of 161 feet per second. This body, then, takes 5 seconds
to ascend, and it would descend in the same time.

Let us repeat, in order that the reader may not imagine that
the above numbers are found to be rigorously true in practice, that
the resistance of the air is an element which much influences the
movements of rising or falling bodies, and that the ratio of their
weight to the surface which they offer to this resistance makes the
result vary. The experiment made by a physicist of the eighteenth
century, Desaguliers, before Newton, Halley, Derham, and many
others, may here be referred to. Having dropped from the lantern
above the dome of St. Paul's different bodies, such as leaden balls
2 inches in diameter, and bladders filled with air, of 5 inches
in diameter, he found that the lead took 4J seconds to fall through
272 feet, the height of the lantern above the ground ; and that
the bladders took 18 J seconds. Now, in vacua, the space would
have been passed through by both bodies in 4J seconds.

As the resistance of the air increases with the velocity of the
fall, it is clear that bodies which fall from a great height, after
having acquired a certain speed, finish their descent with a uni-
form movement. It has been calculated that a drop of water, the
volume of which would be about the T 000>0l00;000th of a cubic inch,
would fall through perfectly calm air with a constant velocity of
5 inches a second, so that it would not travel more than 25 feet
in a minute. This explains the relatively small velocity of rain-
drops, in spite of the considerable height of the clouds from which

34 PHYSICAL PHENOMENA. [BOOK i.

CHAPTER IV.

LAWS OF GRAVITY. — THE PENDULUM.

The Pendulum — Galileo's observations — Definition of the simple pendulum — Iso-
chronism of oscillations of small amplitude — Relation between the time of
the oscillations and the length of the pendulum — Variations of the force of
gravity in different latitudes — Borda's pendulum — Lengths of the pendulums
which beat seconds in London, at the equator, and at the poles — Calculation
of the oblateness of the earth — Experiments proving that the density of the
earth increases from the surface to the centre.

"VTEWTON, seated one day in his garden at Woolsthorpe, saw an
•*•' apple break off from the branch of a tree, and fall at his feet.
It was this simple circumstance which suggested to him his pro-
found researches on the nature of the force of gravity, and which
made him ask whether this mysterious action, to which all terres-
trial bodies are subjected, whatever their height in the atmosphere,
whether at the bottom of valleys or at the top of the highest
mountains, did not extend even to the moon. Thanks to the
meditations of this great genius, we had not long to wait for the
solution of this grand problem : but it was not till twenty years
later tha,t the edifice of which Kepler, Galileo, and Huyghens had
prepared the foundation, which the successors of Newton finished,
and which bears this triumphant superscription — " Universal Gravi-
tation,"— was at last constructed in its majestic beauty.

Is this anecdote, repeated by all biographers of the great man,
really true ? It matters little : the essential point is that it is
probable. But we should be mistaken if we imagined that it was
of a nature to diminish the glory of the philosopher. Such things
had happened millions of times before, to his ancestors and to his
contemporaries. Such a fact as the fall of an apple could only

CHAP, iv.] LAWS OF GRAVITY. 35

excite such thoughts in a mind capable of the highest specula-
tions, and moved by a will powerful enough to be always thinking
them out.

It was a similar occurrence which caused Galileo to undertake
his researches on the motion of the pendulum. He was then pro-
fessor at Pisa, and, as we have before stated, was studying the laws
of falling bodies. " One day," we read, " while present at a religious
ceremony in the cathedral — paying, however, it would seem, very
little attention to it — he was struck by a bronze lamp — a chef-
d'oeuvre of Benvenuto Cellini — which, suspended by a long cord,
was slowly swinging before the altar. Perhaps, with his eyes
fixed on this improvised metronome, he joined in the singing.
The lamp by degrees slackened its vibration, and, being attentive
to its last movements, he noticed that it always beat in the same
time." l

It was this last observation which struck Galileo. The lamp,
when the motion had nearly ended, described smaller and smaller
arcs through the air, the period of swing, however, remaining
the same. The able Italian philosopher repeated the experiment,
and discovered the connection which exists between the period of
oscillation and the length of the cord supporting the oscillating
weight. Huyghens completed this beautiful discovery, and gave the
mathematical law of the motion of the pendulum. Let us try to
give an idea of this law, and show how it is connected with the
theory of gravity.

Imagine a material and heavy point M' (Fig. 14) suspended to one
of the extremities of an inextensible line without weight. These
are conditions which cannot be realised in practice, but they are
accessible in theory. The line being fixed by its upper end, the
action of gravity on the material point M' stretches the line in the
vertical direction, and the system will remain at rest.

Let us now suppose that the string is moved out of the vertical,
still being kept tight and straight, and is then abandoned to itself
in a vacuum. What will happen ?

The action of gravity in the new position in M continues on
the material point: but as this force always acts in a vertical

1 J Bertrand, " Galileo and his Works."

D 2

36 PHYSICAL PHENOMENA. [BOOK i.

direction, and as the string is no longer in that line, the resistance of
the latter cannot completely annul the force of gravity.

The material point, being attracted, will then fall, but as the
string is inextensible, the fall can only be effected along an arc

of the circle having its centre at the
point of suspension A, and its radius
the length of the string A M. It is as
if the point were on an inclined plane,
with its summit at M, and with an
inclination gradually becoming smaller
and smaller. Calculation shows that
the movement will be effected with
increasing velocity, until the time when
the string will have returned to its

FIG. 14.— Oscillatory movement of a

simple penduhim. vertical position ; then, by virtue of its

acquired speed, it will describe an arc

equal to the first, but with decreasing velocity. Arrived at M", at the
same height as the point M, its motion will cease. It will be easily
understood that the material point- will recommence a movement
similar, and perfectly equal to, the first, as the circumstances are
the same, but in the contrary direction. This would be perpetual
motion, if the supposed conditions could be fulfilled.

The ideal instrument we have just described is called the
pendulum — the Simple pendulum, in contradistinction to the real
but compound pendulums, which may be actually constructed and
observed.

The whole movement from M to M" is called a swing or an
oscillation, and its duration or period is obviously the time that
the object takes to make the entire oscillation. It is scarcely
necessary to state that the perpetuity of the oscillations or of the
movement of the pendulum is purely theoretical. In reality, many
causes exist which by degrees destroy the motion, and end by
stopping it. The suspended body is not only a material point, but
generally a metallic lens-shaped disc or ball. The rod is itself
often large, and the resistance of the air destroys part of the motion
of the pendulum at each oscillation. Let us add to these causes
of retardation the friction of the knife-edge on the plane of
suspension. Nevertheless, the laws of the simple pendulum have

CHAP, iv.] LAWS OF GRAVITY. 37

been successfully applied to the oscillations of compound pendu-
lums, and the resistances which necessarily proceed from the
relative imperfection of the pendulums have been taken into
account with every possible precision. These laws, which it is
so important to understand, and which have made the pendulum
the best instrument for the measurement of time, the most precise
indicator of the irregularities which the terrestrial spheroid presents,
and a scale by the aid of which the density of our planet and of
all the bodies of our solar system can be weighed, may now be
stated.

The first law is that discovered by Galileo from observation :
it is as follows : — " The time of very small oscillations of one and the
same pendulum is independent of their amplitude ; the oscillations are
isochronous — that is to say, they are all performed in the same time"

By small oscillations must be understood those the angle of
which is less than four degrees. Within this limit the oscillations
of greater amplitude are made in a very little longer time than
the others, but the difference is very slight, and it is not until
after a great number of oscillations that all the little differences
of which we speak become perceptible.

It is theory, then, which demonstrates the isochronism of pen-
dulum oscillations. But the law is easily 'verified by experiment.
If we carefully count a considerable number of oscillations, and by
a good chronometer measure the number of seconds elapsed, these
two numbers obtained give, by simple division, the time of one
oscillation, which will be found to be the same either at the
beginning or at the end of the experiment.

This equality in the time required for passing through unequal
distances under the influence of a constant force appears singular at
first sight; but on reflecting a little it will be understood, without
further demonstration, that in the case of greater amplitude the
pendulum commences its swing in a direction more out of the
vertical ; the force of gravity, therefore, gives it greater velocity,
by the help of which it soon makes up for the lead which a similar
pendulum would have in describing an arc of less amplitude.

The second law which governs the motion of the pendulum
establishes a relation between the time of the oscillations and the
length of the pendulum.

PHYSICAL PHENOMENA.

[BOOK i.

Let us imagine a series of pendulums, the smallest of which
beats seconds, the others performing their oscillations in 2, 3, 4 . . .
seconds respectively. The length of these last would be 4, 9, 16 . . .
times greater than the length of the first: the times following the
series of the simple numbers, the lengths following the series of
the squares of these numbers. This is expressed in a more general
manner by saying: The periods of oscillation of pendulums are in the
direct ratio of the square roots of their lengths.

Theory and observation agree in demonstrating this important
law : but since we speak of experimental verifications, and since
we know that it is impossible to realize a simple pendulum, it is
time to state how the laws of this ideal pendulum are applied to
the real or compound pendulums.

Pendulums of this kind are ordinarily formed of a "bob," or
spherical ball of metal, with a rod adjusted
in the direction of the centre of figure of the
sphere or of the bob. This rod is fixed at its
upper part into a sharp metal knife-edge, which
rests on a hard and polished plane (Fig. 15).
Such are the pendulums the oscillations of
which control the motion of clocks.

In such a system, what is understood by
the length of the pendulum is not the distance
from the point of suspension to the lower ex-
tremity of the heavy body, but the approximate
distance between this point and the centre
of figure of the ball, when the rod of the pen-
dulum is thin and the ball is made of very
dense metal — platinum, for example. This last
point then takes the name of centre of oscillation.
We will show the reason for this fundamental
distinction.

In a simple pendulum there is only con-
sidered to be one material point; in the com-
pound pendulum their number, whether in the
rod or in the ball, is infinite. It is as if there were a series
of simple pendulums of different lengths compelled to execute
their movements together. Their most distant particles find their

FIG. 15. — Compound
pendulum.

CHAP, iv.] THE PENDULUM. 39

movement accelerated; contrariwise, it is retarded in the case of
those nearest the point of suspension. Between these extremes
there is one particle, the duration of whose oscillations is precisely
equal to those of a simple pendulum of equal length. Calcula-
tion makes us acquainted with the position of this particle in the
bar — that is to say, the point which we have just termed the
centre of oscillation.

Let us now try to understand how it is possible, by means
of pendulum observations, to solve several important questions
which deal with the form of our planet and its physical
constitution.

The periods of the small oscillations of a pendulum depend upon
its length, according to the law we have just stated. But these two
elements also depend on the intensity of the force of gravity in
the locality where the oscillations are performed. Hence it follows
that, if we observe with great precision the number of oscillations
that a pendulum— the length of which is known with rigorous
exactness — executes in a sidereal day, we shall be able to calcu-
late the precise duration of a single oscillation, and thence deduce
the intensity of the force of gravity — that is to say, twice the
space in which a heavy body falling in vacua passes through in a
second This intensity is, in fact, connected with the length of
the pendulum and the period of its oscillation.

It is by this method that the value was found which has been
already given for the latitude of Paris — 9-8094 metres.

This determination once obtained, it is possible to obtain by
calculation the length of the pendulum which beats seconds. This
length is at Paris 0'994 metre, at London 3'2616 feet. Now let us
imagine that an observer travels from the equator to either pole.
As the earth is not spherical, the distance of the observer from the
centre of the earth will vary. Greatest at the equator, it will pro-
gressively diminish, will pass through a mean value, and will be
the smallest possible at the poles themselves. Now, for this reason
alone, the energy of the action of gravity in these different places
must decrease from the poles to the equator. Another influence
will also contribute to diminish the intensity of this force — that
is, the rotation of the earth, the velocity of which, being nil at
the two poles, progressively increases with the latitude, developing

40 PHYSICAL PHENOMENA. [BOOK i.

at each point a greater centrifugal force, which partly counter-
balances the action of terrestrial gravity.1

For these two reasons, the intensity of the force of gravity will
vary in different latitudes. How will our observer perceive it ? By
observing the oscillations of the pendulum, which furnishes us with
two different but equally conclusive methods. The first method
consists in employing a pendulum of invariable length ; the rod
and the bob, soldered together, are fixed to the knife-edge in a
permanent manner. Such a pendulum, having a constant length,
or at least only varying with changes of temperature, will oscillate
more rapidly as the force of gravity is increased; so that, in going
from the poles to the equator, the number of oscillations in a mean

FIG. 16.— Effect of centrifugal force.

day will be smaller and smaller. Thus, a pendulum a metre in
length, which at Paris makes in vacuo 86,137 oscillations in twenty-
four hours, if carried to the poles would make 86,242, and at the
equator would only make in the same time 86,017 vibrations.

The other method is to set a pendulum in motion, to measure
with the greatest care the number of its vibrations, and also its
length at the time of the experiment ; then to deduce the length
of a simple pendulum beating seconds at the same station. The

1 The centrifugal force is rendered manifest in physical lectures by the aid of an
apparatus shown in Fig. 16. Circles of steel rapidly turning on an axis take the
forms of ellipses flattened at the extremity of the axis, the flattening being more
considerable as the velocity of rotation is greater.

CHAP. IV.]

THE PENDULUM.

lengths of the pendulums beating seconds in different places,
compared with each other, enable us to calculate the ratios which
exist between the intensity of the force of gravity at those
places.

We possess a great number of observations, made by one or other
of the two methods in various regions of
the two hemispheres, from the seven-
teenth century to the present time.
The most illustrious men have asso-
ciated their names with these investi-
gations, which are of such importance
to the physics of the globe.

We give here (Figs. 17 and 18) a
sketch of the pendulum employed by
Borda, so well known for the accuracy
of his researches. This is the pendulum
which was used in the observations made
at Paris, Bordeaux, and Dunkirk, by
Messrs. Biot and Mathieu.

Borda's pendulum was formed of a
ball of platinum, suspended by simple
adherence, and by the aid of a metal
cap lightly covered with grease, to a fine
metallic wire, which was attached at its
upper extremity to a knife-edge similar
to that which supports the pendulum-rods
of clocks. The knife-edge rested on two
well-polished fixed planes of hard stone,
the position of which was perfectly hori-
zontal. These planes were themselves
fixed to a large bar of iron attached to
supports fixed in a solid wall, in such a
manner as to obtain perfect immobility.

The oscillations were counted by comparing them with those of
the pendulum of a clock placed against the wall, the movement of
the clock being regulated by the stars. By the help of a telescope
placed at a distance of ten metres, the successive coincidences
of the two pendulums were observed, and from the number of the

17.' — Borda's pendulum. Platinum
sphere and knife- edge.

PHYSICAL PHENOMENA.

[BOOK i.

coincidences and the number of seconds elapsed the number of
oscillations was deduced.

This number having been thus ascertained, the length of the
pendulum was measured by operations of the greatest delicacy, the

Fio. 18.— Borda's pendulum. Measurement of the time of an oscillation by
the method of coincidences.

details of which cannot, be given here. They will, however, be
found in Vol. II. of Blot's "Physical Astronomy."

CHAP, iv.] THE PENDULUM. 43

Having stated the length of the pendulum's beating seconds at
Paris and London, we shall now give the length which calculation
and observation have determined for similar pendulums located at
the poles, equator, and at a mean latitude of forty-five degrees.
The intensity of the force of gravity in these different places — that
is to say, the number of metres indicating the velocity acquired in
a second by heavy bodies falling in vacua — is also shown.

Length of the Intensity of the

seconds pendulum. force of gravity.

At the equator ...... 90i1>3 978103

At the latitude of 45 degrees . 993'52 9'80606

At the poles V 1'V .... 996' 1 9 9'83109

It must hot be forgotten that the variation of the force of
gravity in different parts of the earth depends, as we have before
said, both on the form of the globe — which is not spherical, but
ellipsoidal — and on the centrifugal tendency engendered by the velocity
of rotation. .The force diminishes therefore from the poles to the
equator more than it would do without this rotation. But we know
what proportion must be attributed to each of these causes in the
phenomena observed. By the aid of pendulum observations it has
been found pdssible to calculate the flattening of the earth, and to
predict in this manner the results of geodetic operations, as well,
as to support Clairaut's hypothesis on the increasing densities of
the interior strata from the surface to the centre.

By careful comparisons of pendulum oscillations, executed in
different regions of the globe, it has been found that they sometimes
indicate a force of attraction much greater than that given by calcu-
lation ; while in other regions the intensity is, on the contrary, more
feeble than the elliptical form of the earth would require. As the
excess of the action of gravity has been observed especially in
islands situated in the open sea, whilst the opposite is found to be
the case on the coast, or in the interior, of continents, it has been
concluded that the water-level is somewhat depressed in the middle
of the ocean, and that it rises in the vicinity of large extents of land.1

Here, then, we find the pendulum indicating inequalities in the
curvature of the terrestrial spheroid.

1 Saigcy, " Physique du Globe."
E 2

44 PHYSICAL PHENOMENA. [BOOK r.

By observing the difference of length of the pendulum which
beats seconds at the top of a very high mountain and at the level
of the sea in the same latitude, the density of the globe may be
inferred. Another method to arrive at the density consists in
observing the oscillations of the pendulum at the sea-level and
at a great depth in the interior, or at the sea-level and at the
top of a high mountain. The present Astronomer-Royal, Sir G. B.
Airy, made some experiments in the Harton mines, on the vibra-
tions of two pendulums placed, one at the surface, the other at
the bottom of the mine, at a depth of 420 yards. The latter
moved more quickly than the upper pendulum, and its advance
of two seconds and a quarter in twenty-four hours showed that
the intensity of the force of gravity was increased from the surface
of the earth to the bottom of the mine by about -^^th part
of its value.

This result proves that the density of the terrestrial strata
increases from the surface towards the centre ; since, if it were
otherwise, the attraction due to the interior nucleus would diminish
with depth, and the oscillations of the pendulum would be more
and more slow, which is contrary to the fact. The density of the
strata comprised between the surface and the bottom of the mine
being known, and the connection between this density and that of
the nucleus being deduced from the acceleration observed, the mean
density of the terrestrial globe may be calculated. The same
research has been pursued by other methods, and has given slightly
different results — a fact not at all astonishing in a problem of such
delicacy.

To sum up : the terrestrial globe is acknowledged to weigh
nearly five and a half times more than an equal volume of water.
It is also proved that the density of the concentric strata of which
the earth is formed continues to increase from the surface towards
the centre. Physicists agree in accepting — as an inference from
considerations which cannot find place here — for the density of the
central strata, a value double of the mean density, which in its
turn is nearly double of the superficial strata.

CHAP. V.]

WEIGHT OF BODIES.

CHAPTER V.

WEIGHT OF BODIES— EQUfLIBRTUM OF HEAVY BODIES — CENTRE OF
GRAVITY — THE BALANCE.

Distinction between the weight of a body and its mass — Loss of weight which a
body undergoes when it is taken from the poles to the equator — Centre of
gravity, (1), in bodies of geometric form ; (2), in bodies of irregular form — The
Balance ; conditions of accuracy and sensibility — Balance of precision — Method
of double weighing — Specific gravity and density of bodies.

" On precision in measures and weights depends the progress of chemistry, physics, and physiology.
Measures and weights are the inflexible judges placed above all opinions wliich are only supported by
imperfect observations." — J. MOLESCHOTT, La Circulation de la Vie : Indestrnctibilite de la Matibre.

EAVITY acts in the same manner on all bodies, whatever their
VT form or size, or whatever the nature of their substance. This
follows from the equal velocity which all bodies acquire in falling
from the same height and in the same
place. A heavy body, then, may be
considered as the aggregation of a
multitude of material particles, each
of which is acted on individually by
gravity (Fig. 19).

All these equal forces are parallel,
and thus produce the same effect as a
single force equal to their sum applied
at a certain point. This resultant of all
the actions of gravity is the weight of
the body. The point where it is applied,
and which is called its centre of gravity,
is that which must be supported, in
any position of the body, in order that the latter may remain in

FIG. 19.— Weight of a body
of gravity.

46 PHYSICAL PHENOMENA. [BOOK i.

equilibrium. The centre of gravity is not always situated iii the
interior of the body: in some cases it falls outside it.

Although for simplicity's sake we used the word weight in the
first chapter as a synonym for gravity, the force of gravity must not
be confounded with weight : and it is also important to distinguish
weight from mass. Mass, sometimes, is described as the quantity
of matter which a body contains : but this definition is vague, and
does not express the difference which exists between the two terms.
An example will explain the precise sense which is given to this
word in physical inquiries.

Let us take a heavy body — a piece of iron, for example. To
determine its weight, let us suspend it to a spring, or dynamometer
(see Fig. 1), such that its degree of tension will show the intensity of
the action of gravity on the body. Let us notice the divided scale —
the exact point where the upper branch of the instrument stops ;
and let us suppose that this first observation is made, for instance,
in the latitude of Paris.

Now transport the piece of iron and the dynamometer either
to the equator or towards the poles. The intensity of the force of
gravity is no longer the same: the spring will be less extended in
one case, and more so in the other. The weight, as we ought to
expect, after what we know of the variations of the force of gravity,
has changed. And nevertheless we are dealing with the same
quantity of matter : it is the same mass which, in the three cases,
has been used for the experiment.

Thus, then, the quantity of matter — the mass — remaining the
same, the weight varies, and in the same ratio as the intensity of the
action of gravity varies ; so that that which remains constant is the
ratio, which should, for this reason, serve as a definition for the mass.

This variation in the weight of bodies when they are transported
from one place to another in a different latitude would equally take
place if the bodies were to change their altitude : that is, if their
height above or below the sea-level were to be changed, their
masses remaining always constant. But this change we shall not
be able to piove by the aid of balances, because in these instruments
equilibrium is produced by bodies of equal weight, and the variation
in question will take place both in the weight to be measured and
in the weight which is used as a measure.

CHAP. V.]

WEIGHT OF BODIES.

Calculation shows that a mass weighing one kilogramme, or
1,000 grammes, at Paris, would not, when taken to the equator, pull
the dynamometer farther than 997108 gr. The same weight taken
to either pole would pull it as far as a weight of 1000'221 gr. at Paris.

Let us now return to the centre of gravity. It may be interest-
ing, and moreover it is often useful, to know the position of the
point, which, being fixed or supported, the body remains in equilibrium
when it is subjected to the action of gravity only. When the matter
of which the body is composed is perfectly homogeneous, and when
its form is symmetrical or regular, the determination of the centre
of gravity is simply a question of geometry. Let us take the most
ordinary cftses.

FIG. 20. — Centres of gravity of parallelograms, a triangle, a circle, a circular ring, and an ellipse.

A heavy straight bar has its centre of gravity at its point of
bisection. In reality, the material bar is prismatic or cylindrical,
but in the case where the thickness is very small in comparison
with the length we may neglect it without inconvenience. The same
remark is applicable to very thin surfaces, and they are considered as
plane or curved figures without thickness. The square, rectangle,
and parallelogram have their centres of gravity at the intersections of
their diagonals (Fig. 20). The triangle has it at the point of inter-
section of the lines which fall from the summit of each angle on
to the middle of the opposite side, — that is to say, at one-third the
distance of the vertex from the base, measured along any of these
lines. If these surfaces were reduced to their exterior contours, the
position of the centre of gravity would not be changed

PHYSICAL PHENOMENA.

[BOOK i.

The centre of figure of a circle, a circular ring, or of an ellipse,
is also its centre of gravity. Eight or oblique cylinders, regular
prisms, and parallelepipeds (Fig. 21) have their centres of gravity

FIG. 21.— Centres of gravity of a prism pyramid, cylinder mm cone.

at the middle points of their axes. That of the sphere, and the
ellipsoid of revolution, is at its centre of figure (Fig. 22). To find
that of a pyramid, or of a right or oblique cone, a line must be drawn

FJG. 22. — Centres of gravity of an ellipsoid and a sphere of revolution.

from the vertex to the centre of gravity of the polygonal base, and
the centre lies along this line at one-fourth of the distance of the
vertex from the base.

These statements are true for homogeneous bodies of geometrical

CHAP. V.]

EQUILIBRIUM OF HEAVY BODIES.

form. But, in nature, the form is often irregular, or the material of
the body is not equally dense in all its parts. In such cases, the
determination of the centre of gravity is made by experiment. A
simple way of finding it is by the suspension of the body by a
string. When it is in equilibrium, the centre of gravity will lie along
the prolongation of the string, the direction of which is then vertical.
A second determination must be made by suspending the body
by another of its points; this furnishes a new line, in which the
centre of gravity lies. The intersection of these two lines, then,
gives the centre of gravity (Fig. 23), which may be sometimes
inside, sometimes outside the heavy body.

The definition of the centre of gravity indicates that, when this
point is supported or fixed, provided
that all the material points of which
the body is composed are rigidly united,
equilibrium is secured. But this condi-
tion is difficult to fulfil, as very often
the centre of gravity is an interior
point, by which the body cannot be
directly fixed or supported.

If the suspension is made by a string
or flexible cord, equilibrium will estab-
lish itself; the centre of gravity will
then be on the vertical line passing
through the point of suspension. If,
when this position is obtained, the body
is disturbed, it will form a compound
pendulum, will execute a certain number of oscillations, and
will again come toarest. This is what is called stable equilibrium,
and it is an essential condition of this kind of equilibrium that
the position of the centre of gravity be lower than the point of
suspension, so that when the body is disturbed the centre of
gravity rises.

In general, in order that a heavy body be in equilibrium under
the action of gravity, it is necessary and sufficient that its centre of
gravity be in the vertical line passing through the point of support
when it is suspended from a point above it, or within the area of the
plane of support if it rests on fixed points. Figs. 24 'and 25 give

(

t*'w. 23.— Experimental determination of
the centre of gravity of a body of
irregular form or non-homogeneous

structure.

PHYSICAL PHENOMENA.

[BOOK i.

examples of the latter. The Leaning Towers of Bologna and Pisa
(Fig. 3 represents the second of these structures) are singular cases in
which the equilibrium is preserved, owing to the circumstance that the

Fio. 24.— Equilibrium of a body supported on a plane by one or more points.

centre of gravity of the edifice is in the vertical line falling within
the base. But it is to be understood that the materials of which
these towers are built must be cemented together in such a manner,

FIG. 2o. — Equilibrium of a body resting on a plane by three support*.

that each of them cannot separately obey the force which would
cause its fall.

The water-carrier and porter, represented in Fig. 26, take posi-
tions inclined either to the side or the front, so that the centre
of gravity of their bodies and the load which they sustain, taken
together, is in a vertical. line falling within the base formed by their

CHAP. V.J

CENTRE OF GRAVITY.

feet. The same condition is fulfilled by the cart (Fig. 27), which
travels transversely along an inclined road : it remains in equilibrium
so long as the centre of gravity is vertically above the base com-
prised between the points where the wheels touch the ground. It

Fu;. M.— I'ojsitions uf equilibrium of persons currying loads.

would upset if this were not so, either from too great au inclination
of the road, or from a too rapid movement impressed on the vehicle
and its centre of gravity, flinging the line outside the wheel.

Fio. 27. — Equilibrium on an inclined plane.

When a body is supported by a horizontal axis, around which it
can turn freely, its equilibrium may be either stable, neutral, or
unstable. It is stable, if the centre of gravity is below the axis;

52 PHYSICAL PHENOMENA. [BOOK i.

neutral, if this centre is on the axis itself ; and unstable, if the centre
of gravity is above the axis. Fig. 28 furnishes an example of each
of these cases.

The determination of the centre of gravity of one or more heavy
bodies is a problem which frequently finds numerous applications in
various industrial arts. But another question, no less interesting and

FIG. 28. — Stable, neutral, and unstable equilibrium.

useful, is to determine that resultant of which the centre of gravity
is the point of application, or, to use the common expression, to
weigh bodies.

The instruments destined to this use have received the name of
Balances, or Scales. The Balances used are very varied in their forms
and in their mode of constructions, and we shall describe them in
detail when we treat of the Applications of Physics. Here we shall
confine ourselves to the description of the delicate balances used
in scientific researches.

The principle on which their construction is based is this : —
A lever, a rigid, inflexible bar, resting at its centre on a fixed
point, on which it can freely oscillate, is in equilibrium when
two equal forces are applied to each of its two extremities.

To make a lever of this kind serve as a balance, it is indis-
pensable that certain conditions be attended to in its construction.

It is necessary, first, that the two arms of the lever or beam
A o, OB, be of equal length and of the same density, in order to

CHAP. V.]

CENTRE OF GRAVITY.

PlG. 29.— Scales.

produce equilibrium by themselves. The two scales, in one of which
is placed the standard weight, in the other the body to be weighed,
ought also to be of exactly the same weight.

In the second place, the centre of gravity of the system ought
to be below the point or axis of
suspension, and very near to this
axis. It follows from this second
condition, that the equilibrium
will be stable, and that the oscil-
lations of the beam will always
tend to bring it back to a hori-
zontal position, which is the in-
dication of the equality of weight
between the bodies placed in the
two scales.

These two conditions are neces-
sary, in order that the balance
be exact ; but they are not suf-
ficient to make it sensitive or
delicate — that is, to cause it to indicate the slightest inequality in
the weights by an unmistakable inclination of the beam.

In order that a balance be very exact and delicate, it is further
necessary : 1st. That the point, or axis of suspension, of the beam
and of the two scales should be in the same right line. In this
case, the sensibility is independent of the weights on the scales.
2nd. That the beam be of a great length, and as light as possible ;
which makes the amplitude of the oscillations greater for a given in-
equality of the weights. This is the reason which necessitates the
centre of gravity of the balance being very near the axis of suspension
of the beam, without, however, absolutely coinciding with it. Let us
now show how these conditions are realized in the delicate balances
used by physicists and chemists.

The beam is made of a lozenge shape, formed out of a metal plate
of steel or bronze, cut away in such a way as to diminish its weight
without increasing its flexibility. Through its centre passes a steel
knife-edge, the horizontal edge of which forms the fulcrum of the
beam. This edge rests on a hard and polished plane — of agate, for
example. The two extremities of the beam carry two other very

54 PHYSICAL PHENOMENA. [BOOK i.

small knife-edges, which, being horizontal and parallel to those
of the principal one, support movable steel plates, to which are
attached the rods which hold the cups or scales.

The three edges which we have described must be placed exactly
in the same plane, and their distances from each other must be
perfectly equal. In the middle and above the beam, two buttons
are fixed, one above the other, one of which is made like a nut,
so that it can be screwed up or down at • will. It is used to
raise or lower the centre of gravity of the balance in such
a way as to bring it nearer to or further away from the axis of

FK;. 30. — Chemical hfdancc : the beam.

suspension, and thus give to the balance the degree of sensibility
required.

Above and in front of the middle knife-edge, the beam carries a
long metallic rod or needle, which oscillates with it, and its position
is exactly vertical when the plane, formed by the three axes of sus-
pension, is horizontal. The lower extremity of this needle moves
over an ivory arc, the zero division of which corresponds to this
last position, and determines it. On either side of zero, equal
divisions indicate the amplitudes of the oscillations of the needle :
if these amplitudes be equal on each side, we are assured of the
horizontality of the bf/am and of the equality of the weights in the
scales.

CHAP. V.]

THE BALANCE.

A balance thus constructed should be placed on a firm plane ;
and by the use of the elevating screws placed at the foot of the
instrument, and by observing the needle, its position must be made
exactly horizontal before beginning work. To avoid the influence
of currents of air and the deterioration proceeding from dampness or
other atmospheric agents, the balance is also inclosed in a glass case,
which is shut daring the weighing, and is only opened to insert or

FIG. 31. — Chemical balance.

remove the weights and the suostances to be weighed. Chloride of
calcium is also placed in the case to absorb the moisture. Moreover,
when the apparatus is not in use, a metallic fork is made to raise
the beam by means of rackwork inclosed in the column, so that
the knife-edges may keep their sharp edges, which, without this
precaution, the pressure would in time render dull.

56 PHYSICAL PHENOMENA. [BOOK i.

We now see with what precision the conditions of exactitude
of a balance destined to scientific uses, such as the instrument just
described, are realized. This precision is indispensable in the
delicate determinations required in physical researches and modern
chemistry. But they do not suffice : the operator must also add
the ability which experience produces, and precautions on which
we cannot enter.

It is unnecessary to state that the precision of the balance would
be completely useless if the weights were not themselves rigorously
exact. Sometimes, besides the series of mean weights, the operator
possesses another series of small weights, which he has carefully
constructed himself, of very fine platinum wire, which he uses for
weights lower than a gramme, as decigrammes, centigrammes, and
milligrammes.

At the present time, balances are made delicate enough to detect
a milligramme ('0154 grain) when each scale is charged with five
kilogrammes (13*39 lb.). In the balances used in chemical analysis,
tenths of milligrammes ('00154 grain) even are weighed; but then
the total charge must be very small, two grammes for example.

Physicists frequently employ the method of double weighing, to
remedy any inequality in the arms of the beam. They place
the body to be weighed in one of the scales, and then establish equi-
librium by putting in the other scale an ordinary tare formed of
leaden shot. In this state, if the arms be not exactly the same
length, the apparent equilibrium does not prove the equality of the
weights. But if, on removing the body, it is replaced by weights
graduated until equilibrium be again established, it is easily under-
stood that these weights exactly represent the weight sought for,
since they produce the same effect as the body itself does under the
same conditions.

It will be seen further on, that the weight of a body is modified
by the medium in which it is weighed, so that it is lessened by the
weight of the fluid which it displaces. On the other hand, its volume
varies with the temperature, and consequently the same body does
not always displace the same quantity of fluid. Hence the neces-
sity of taking account of these elements of variation, unless the
precaution is taken of weighing in a space void of air — that is to
say, in vacuo.

CHAP, v.] WEIGHT OF BODIES. 57

The unit of weight generally adopted by scientific men of all
countries is that of the metric system of weights and measures —
the kilogramme.

A cubic decimetre of distilled water, weighed in vacua at the
temperature of four degrees centigrade above its freezing-point,
in the latitude of forty-five degrees, and at the level of the sea,
weighs one kilogramme. Such is the exact definition of the unit
of weight. It must not be forgotten that, if the weight varies with
the latitude and with the height above the level of the sea, the
variation does not manifest itself in a balance, because it affects in
the same manner the weights placed in both scales. These causes
of error may, therefore, be neglected when the balance is employed.

We may state also, in bringing this chapter to a close, what is
understood by specific gravity and density : further on, we shall see
how the values in question are experimentally determined. Equal
volumes of different substances have not the same weight; a block
of stone weighs more than a piece of wood, and less than a piece
of iron, of the same dimensions ; this is a fact easily proved, and
known by every one. Let us suppose that we take, as the unit
of volume of each, the cubic decimetre, for instance, and weigh
them all at a constant temperature, the values obtained will be what
are called the absolute weights of these substances.

The absolute weights would vary, if the unit of weight were
changed, but their relations would remain invariable. It is then
usual to take one of them for unity: the weight of water is thus
chosen, because water is a substance spread all over the earth, and
it is easily procured in a state of purity. The weight of a cubic
decimetre of any other substance, expressed in units each of which
is the weight of a cubic decimetre of water (a gramme) is called
relative or specific weight, or specific gravity.

In making similar comparisons between the masses of different
substances taken in unit volumes of each, we determine also what
is called the relative density of substances. The numbers thus
obtained are precisely the same as the specific gravities, they
ought not to be confounded one with the other, under the common
denomination of density.

58 PHYSICAL PHENOMENA. [BOOK i.

CHAPTER VI.

WEIGHT OF LIQUIDS. — PHENOMENA AND LAWS OF EQUILIBRIUM :

HYDROSTATICS.

T)HENOMENA the most curious and the most worthy of attracting
-L our attention are daily passing before our eyes without our
taking any notice of them, much less considering the causes which
give rise to them. Such are, for example, the different appearances
under which we see bodies, sometimes solid, sometimes liquid,
sometimes gaseous, and sometimes passing successively through
the three states. In what does ice differ from water, and how
does the latter transform itself into vapour ? What difference is
there between the arrangements of the molecules which constitute
these three forms of one substance ? These are questions very
difficult of solution, on which science possesses few data, which
we will review in the several chapters of this work. We shall
confine ourselves here to those which are indispensable to the
understanding of the phenomena we are about to describe.

That which distinguishes a solid body when it is not submitted
to mechanical or physical forces capable of breaking it, or of
making it pass into a new state, is its constant form. Let us con-
sider a stone or a piece of metal. Its particles are so solid that they
keep their mutual distances, separating from each other only under
an exterior force, more or less strong. It follows that the position of

CHAP. VI.]

WEIGHT OF LIQUIDS.

the centre of gravity of the body remains invariable, and that what-
ever movement a stone receives, whether it is thrown into the air or
falls under the action of gravity, all its particles will participate in
the motion at the same time and in the same manner. Cohesion is
the force which thus unites the different molecules of a body one to
the other.

It happens, when a solid body is reduced to very fine particles — to
small dust— that this cohesion appears to be, if not annulled, at least
considerably diminished. Hence it is that it n

is difficult to maintain a heap of sand in the
form of a high cone : the grains slip one over
the other, and their movement along the slope
of the mass is somewhat analogous to the flow-
ing of a liquid on an incline. This analogy
appears still more striking when we fill a vessel
with fine powder, and make a hole in the
bottom. The flow resembles that of a liquid
(Fig. 32), but in appearance only, for each
grain, however small it be, is a mass which
has all the properties of a solid body, and,
indeed, does not differ from one.

What then, from a physical point of view,,
is the special characteristic which distinguishes
liquids from solids ?

It is that, whilst in the latter molecular cohesion is strong enough
to prevent the movement of its different particles, in liquids, on the
contrary, this force is nothing, or nearly nothing. Hence the extreme
mobility of their particles, which slide and roll one over the other
under the action of the slightest force. In consequence of this
mobility, a liquid mass has in itself no definite form ; it takes,
when in equilibrium, the form of the vessel or natural basin which
contains it, the walls of which prevent it from moving under the
action of gravity.

It must not be imagined from this that there is no cohesion
in liquids. When a liquid mass is in motion, its particles do indeed
change place, but they are not isolated or separated, as happens
in the case of sandy matters : the distance between the particles
does not change, and, if the form is modified, the volume remains

F 2

FIG. 3-2.— Flowing of
sand.

PHYSICAL PHENOMENA.

[BOOK r.

FIG. 3S. — Cohesion of liquid
molecules.

invariable. When a solid disc is applied to the surface of a liquid
which moistens it (Fig. 33), it requires a certain effort to separate

it from the liquid, and the liquid stratum
which the disc takes with it is a proof that
this effort was necessitated by the force
which united the liquid molecules to
each other. It would be the same if a
rod were dipped in a liquid susceptible
of moistening the substance of which the
rod is formed. On drawing it out, a
drop of liquid would be seen suspended
at the end. Lastly, the spherical form
which dew-drops, when deposited on leaves, or small drops of
mercury lying on a solid surface (Figs. 34 and 35), present, is
explained by the preponderance of the molecular cohesion over

the action of gravity, which other-
wise would tend to spread out the
small liquid masses in question
over the surfaces which sustain
them. Nevertheless, this cohesion
is very slight, as may be shown by
the mobility of the particles and
the facility with which the cohesion
is overcome : a mass of water pro-
jected from a certain height falls to
tiie ground in a shower of spray,
due,- as we have already seen, to
the resistance of the air.
Moreover, there is a great difference in this respect between
various liquids. Some are viscous, and their molecules are but slowly
displaced, requiring time to take the form of the vessels which
contain them; such are resins, and sulphur at certain temperatures.
Soft bodies are in a kind of transition state between solids and
liquids.1 Other bodies, such as the ethers and alcohols, possess

1 The cohesion of the particles which form solid bodies can be overcome by
sufficient pressure. Some experiments of great interest made by M. Tresca have
proved the fact— in appearance paradoxical — that the hardest solids can, without
changing their state, flow like liquids under great pressure.

FIG. 34.— Spherical form ot dew drops.

CHAP, vi.] WEIGHT OF LIQUIDS. 61

a great degree of liquidity, and pass with the greatest facility
into a state of vapour. Lastly, there is a certain number of liquids
like water, in a degree of liquidity which is a mean between these
two extremes. We shall see further on that heat and pressure have
a very important influence on these different states.

Whatever these differences may be, the phenomena which we are
about to pass under review are manifested by all liquid bodies, to

Fio. S5.— Cohesion of liquid molecules ; drops of mercury.

degrees which vary only according to their more or less perfect
liquidity.

Most people have heard of the celebrated experiments made at
the end of the eighteenth century by the physicists of the Academy
del Cimento, of Florence, on the compressibility of liquids. Does
water, or more generally speaking, does any liquid change its volume,
when submitted to a considerable mechanical pressure ? Such was
the question which these men asked themselves, and which they
believed they solved negatively. They caused a hollow silver sphere
to be made, filled it with water, and immediately hermetically
sealed it. Having then strongly compressed it, they saw the water
oozing through its walls. They made other experiments with the
same result, and they concluded that liquids do not diminish in
volume under the action of the greatest mechanical forces, or, in
otl-ier words, that they are incompressible.

But more recent experiments . have invalidated those of the
Florentine Academicians. The compressibility of water and many
other liquids has been demonstrated. Canton in 1761, Perkins in
1819, Oersted in 1823, and, more recently, Despretz, Colladon and
Sturm, Wertheim and Kegnault, have measured with continually
increasing accuracy the diminution of volume brought about in
sundry liquids subjected to a determinate pressure. We shall see
later that this diminution is extremely slight,— so slight that

62 PHYSICAL PHENOMENA. . [BOOK i.

it need not be taken into account in the study of hydrostatic phen-
omena. We will now give a description of the more important of
these phenomena.

Imagine two cylinders of unequal diameter communicating at
their bases by a tube (Fig. 36). Two perfectly fitting pistons move
freely in the interior of each of them, and the tube and the
cylinders below the pistons are filled with water. We find by

this experiment that, in order to obtain
16JC equilibrium in the instrument, if the
charge of the piston of the small
cylinder, added to its own weight, is, for
example, one kilogramme, or one pound,
the largest piston must be charged, its
own weight included, by as many times
one kilogramme or one pound as the sur-
face of the large cylinder contains that of
the small one.

In the example represented in Fig. 36

FIG. 36.— Principle of tlie hydraulic

press. one kilogramme balances sixteen. It

seems as if the pressure exercised by the

surface of the small piston were transmitted, without any modifi-
cation of its energy, through the liquid to each equal portion of
the surface of the large one.

Such is, in fact, the principle on which rests the construction of
a machine of the greatest utility, which will be described in the
Applications of Physics, and which is known under the name of the
hydraulic press or ram. The discovery of this principle is due to
Pascal : it is a consequence of the mobility and elasticity of liquid
particles. It may be formulated as follows : — Pressure, exercised on
a liquid contained in a closed vessel, is transmitted with the same energy
in all directions. By this it must be understood that if we take
on the liquid or on the interior walls of the vessel a surface equal
to that on which the pressure is exercised, this surface will undergo
a pressure exactly equal to the first ; if the surface which receives
the pressure is double, triple, quadruple, &c., of that which transmits
it, it will support a double, triple, and quadruple pressure. So that,
if we open in the sides of the vessel orifices of any dimensions,
it is necessary, to maintain equilibrium, to exercise on the pistons

CHAP. VI.]

WEIGHT OF LIQUIDS.

FIG. 37. — The pressure exercised
on one point of a liquid is
transmitted equally in every
direction.

which shut these orifices pressures proportional to their surfaces
(Fig. 37). In order to prove this by experiment, it is necessary, in
measuring the pressures exercised or transmitted, to take into account
the pressures which proceed from the force
of gravity, or that which the liquid ex-
ercises on itself or on the walls -of the
vessel by its own weight. The experiment
shown in Fig. 36, and actually realized
in the hydraulic press, is an evident cfon-
sequence of Pascal's principle.

We have seen — and it is a fact which
every one can prove by observation — that
the direction of the plumb-line is perpen-
dicular to the surface of a liquid at rest.

It can be easily understood that it could not be otherwise. In
fact, when the surface of a liquid is not plane and horizontal, a
particle such as M (Fig. 38) finds itself on an inclined plane,
and, in virtue of the mobility proper to liquids, it glides along the
plane under the influence of its own weight. Equilibrium will
be impossible until the cause of the
agitation of the liquid having ceased,
the surface becomes by degrees level,
and is exactly plane or horizontal.
The large liquid surfaces of the seas,
lakes, and even of pools, are rarely in
repose. The agitations of the air, high
winds, or light breezes, are sufficient

to produce the multitudes of moving prominences, which are
called waves, or simple ripples. But if, instead of taking into con-
sideration a small portion only, we embrace with the sight or in
thought an extent of sufficient radius. — or if we contemplate this
extent from a considerable distance, — the inequalities are effaced over
the whole ; the liquid appears to be at rest ; and its surface is
clearly a horizontal plane.

We must always bear in mind that the earth is spheroidal ; that
the verticals of the different places are not parallel ; that the real
surfaces of the seas and great lakes participate in its curvature, as
is proved by various optical phenomena described in one of our

FIG

I. — Tlie surface of liquids in
repose is horizontal.

PHYSICAL PHENOMENA.

[ROOK i.

preceding works.1 But this only serves to confirm the essential
condition of the equilibrium of a liquid contained in a vessel and
submitted to the action of the force of gravity only.

The exterior surface of a liquid in equilibrium is always level,
or plane and horizontal. This is on the exterior. Let us now see
what happens in the interior. Each liquid particle possessing
weight, it originates a pressure which is exercised vertically, and
ought to transmit itself in every direction to the other portions
of the liquid, and to the walls of the vessel which contains it.

FIG. 39.— Pressure of a liquid on the bottom of the vessel which contains it.

What is the result produced by the pressure of all the particles ?
The following experiment will answer this question.

Let us take a cylindrical vessel, without a bottom, supported by
a tripod of a certain height (Fig. 39). A flat disc, in the form of
a plate, suspended by a wire attached to one of the arms of a
balance, is applied exactly to the lower edges of the cylinder, so

1 See " The Heavens."

CHAP, vi.] WEIGHT OF LIQUIDS. 65

as to form a bottom to it. In the other scale, a counterpoise is
placed equal to the difference between the weight of the cylinder
and that of the disc. Lastly, standard weights are added, which
cause the disc to press against the bottom edge of the cylinder.
Water is then poured into the latter. By degrees the pressure of
the liquid on the movable bottom increases ; when it has become
equal to the added weights, the least excess of liquid detaches the
disc, and the water flows out. But the pressure diminishes by this
outflow, and the disc again adheres closely to the cylinder. A
pointer which touches the surface of the water marks its level at
the moment of equilibrium.

It is seen from this first experiment, that, as we should expect,
the pressure exercised oil the bottom of the vessel is precisely equal to
the weight of the liquid.

If now we repeat the experiment with a vessel with the same
sized orifice at bottom as the cylinder, but wider at the top, and
consequently of much greater content, we find identically the same
result — that is to say, the same weight counterpoises a column of
liquid of the same height. The result is the same if a vessel nar-
rowed at the top is employed, provided that the surface of the base
remains the same.

Thus, the pressure exercised by the weight of a liquid on the
bottom of the vessel which contains it is independent of the form
of the vessel, but proportional to the height of the liquid, and lastly,
equal to the weight of a liquid column of the same height, having
the bottom of the vessel for a base.

The experimental demonstration of the first part of this law
may also be shown by the aid of Haldat's apparatus; but the
measure of the pressure is not directly given, as in the first method.
It is shown by the elevation of a column of mercury in a tube,
as shown in Fig. 40.

If, instead of inquiring the degree of pressure on the bottom
of the vessel, we wished to find that exercised on the surface of
a liquid stratum, or the sides of the vessel, this pressure would be
found to be the same, with equal surfaces and the same depth ; for
it is also measured by the weight of a vertical liquid column, having
the pressed surface for its base, and for its height the distance of
the stratum from the surface of the liquid.

PHYSICAL PHENOMENA.

[BOOK i.

The following experiment demonstrates this law in the case of a
surface taken on an interior horizontal stratum : —

A cylinder, open at the two ends, and furnished with a disc
or movable covering, which serves it as a bottom, is plunged ver-
tically into a vessel full of water (Fig. 41). The hand is obliged to
exert an effort in introducing the cylinder, which proves that the
liquid exercises an upward pressure which holds the disc against

FIG. 40. — Pressure of a liquid on the bottom of a vessel : Hal;lat'>-

the edges of the cylinder and prevents the water from getting in.
If, now, water is poured into the tube, equilibrium continues as
long as the interior level is lower than the exterior one. At
the moment when equality is attained in the levels, and even a
little before, on account of the weight of the disc, the latter
gives way, and equilibrium is destroyed. The same result is
always produced to whatever depth the cylinder is immersed.
Hence this law : —

CHAP. VI.]

WEIGHT OF LIQUIDS.

In a liquid in equilibrium under the sole action of the force of
gravity, the pressure on a definite point of the same horizontal stratum
is constant ; it is measured by the iveight of a liquid column having for
base the area of the surface under pressure, and for height the vertical
depth of the stratum.

The lateral pressures on the walls are measured in the same way.
It must be added that their pressure is always exerted normally,
that is to say, perpendicularly to the surface of the walls, so that it is
exerted in a direction contrary to the action of gravity, if the wall is
horizontal above the liquid.

FIG. 41. — Pressure of a liquid on a horizontal
stratum.

FIG. 42. — The pressures of liquids «re normal
to the walls of the containing vessel.

We will give some experiments which prove the existence and the
directions of these pressures.

A cylinder (Fig. 42) is terminated by a very thin metallic ball
pierced with holes in all directions. If it be filled with water, it will
be seen to spout out through all the orifices, and the direction of the
jet is always normal to the portion of surface whence it escapes. In
the rose of a watering-can the water escapes in virtue of this property
of liquids to press laterally against the walls of the vessels which
contain them.

The hydraulic tourniquet shows the lateral pressure exerting itself

PHYSICAL PHENOMENA.

[BOCK T.

in two opposite directions at the two extremities of a doubly
curved horizontal tube (Fig. 43). If this tube were not open, the
lateral pressure on the end would be counterbalanced by an equal and
contrary pressure at the elbow, and the instrument would remain at

Fio. 43. — Hydraulic, tourniquet.

rest ; but the orifices at each extremity permit two liquid jets to escape,
and as the pressure on each elbow is no longer counterbalanced, a
backward movement follows and a rotation of the tube is set up.
The pressures, lateral or. otherwise, exerted normally on the walls

explain all that is peculiar in the
equality of pressure on the bottom
of vessels of different forms. In
a wide-mouthed conical vessel,
the lateral walls support the ex-
cess of the total weight of the
liquid over that of the column

FIG. 44. — Hydrostatic paradox.

which measures the pressure on

the bottom. In a narrow-topped vessel, the walls are subjected to
pressures in a direction opposed to that of the force of gravity, and

CHAP. VI.]

WEIGHT OF LIQUIDS.

the amount of this pressure is precisely equal to that which is
wanting to form the liquid cylinder, the weight of which is equivalent
to the pressure on the horizontal bottom of the vessel (Fig. 44).

Thus is explained the phenomenon, which at first appears so singular,
of liquid columns
very different in
weight when they
are measured in
the scale of a ba-
lance, nevertheless
exerting the same
pressure on a unit
of surface in the
bottom of a vessel,
if the weight of the
liquids be equal.
Pascal proved this
fact, which is
called the hydro-
static paradox. He
burst the staves of
a solidly construc-
ted barrel, filled
with water, the
1) u n g - h o 1 e o f
which was sur-
mounted by a very
narrow, high tube,
and he did this
by simply tilling
this tube with
water

; that is to
say> by adding to
the whole weight
an insignificant

FIG. 45. —Hydrostatic paradox. Pascal1:

addition (Fig. 45). The walls of the barrel had to support the
same pressure as if they had been surmounted by a mass of water
having a base equal to the bottom of the barrel and the same height

PHYSICAL PHENOMENA.

[BOOK i.

as the length of the column of water in the tube. One kilogramme
of water can produce, in this manner, the same effect as thousands
of kilogrammes.

If, in the same vessel, we introduce liquids of various densities, not
susceptible of mixing — for example, mercury, water, and oil — these
liquids will range themselves in the order of density. Moreover,

when equilibrium is established (Fig. 46),
the separating surfaces are plane and
horizontal.

This experimental fact might be fore-
seen, for the equilibrium of a single
liquid requiring, as we have before seen, a
horizontally of surface, this equilibrium
is not broken, when this surface also
supports at every point a pressure due
to a superposed liquid.

It is possible, with great precautions,
to obtain equilibrium with two liquids of
nearly equal densities, by placing the
heavier one uppermost, but the equili-
brium is unstable, and the least agitation
again establishes the order of densities.

This is the reason of the existence, in the fiords or gulfs on the
Norwegian coasts, of the sheets of fresh water brought by the rivers,
which have been observed ; these maintain themselves on the surface
of the salt water without mixing with it, although sea-water is
heavier than fresh water. Vogt records that in one fiord one of
these sheets was I1 50m. deep. This phenomenon is only possible
in calm localities, as the agitation caused by winds would soon mix
the fresh water with the salt. The same fact has been noticed in
the Thames, the tides bringing the sea- water to a great distance in
the bed of the river.

The equilibrium of a liquid contained in a vessel and submitted
to the action of gravity alone is independent of the form of the
vessel. Hence this very natural consequence, that a liquid rises to
the same height in two or more vessels which communicate one with
the other. Experiment shows that the level is always the same in
different tubes or vessels connected together by a tube of any form

CHAP. Vf.]

WEIGHT OF LIQUIDS.

whatever, provided always that the diameter of each be not too
small (Fig. 47).

It is this principle which serves as a basis to the theory of arte-
sian wells, the construction of the fountains which play in public
or private gardens, and the distribution of water in our towns.
We shall return to these interesting applications in another
volume. It is the principle only which interests us here. The
water which arrives at the orifice of an artesian well often proceeds
from very distant reservoirs, forming as it were subterranean rivers,
the level of which, at the source, is higher than at the point of
outflow. The pressure is thus transmitted to a distance, and the

FIG. 47.— Equality of height of the same liquid in communicating vessels.

jet which follows would rise precisely to the same height as the
original source, were it not for the resistance of the air and the
friction to which the ascending column is subject in its passage.
The same thing happens with the jets of water fed by a
reservoir higher than the basin and communicating with it by
subterranean pipes.

If two communicating vessels contain liquids of different den-
sities, the heights are no longer equal (Fig. 48).

Let us first try mercury. The level will be established in the
two tubes at the same height. In the left-hand tube, let us now

PHYSICAL PHENOMENA.

[BOOK i.

pour water. The mercury will rise in the right-hand tube, under
the influence of the pressure of the new liquid. Equilibrium having
been established, it is easily proved that the heights of the level
of the water and of the mercury, measured from their common

FIG. 48. — Coiinmuiicating vessels. Heights of two liquids of different densities.

plane of separation, are in the inverse ratio of their densities. For
example, if the mercury rises three millimetres, the column of water
will have a length of 40-8 millimetres ; that is to say, a length
DV6 times greater. Now, a volume of water weighs 13-6 times less
than an equal volume of mercury.

CJAP. vii.] EQUILIBRIUM OF BODIES IN LIQUIDS. 73

CHAPTER VII.

EQUILIBRIUM OF BODIES IMMERSED IN LIQUIDS. — PRINCIPLE OF
ARCHIMEDES.

Pressure or loss of weight of immersed bodies — Principle of Archimedes — Experi-
mental demonstration of this principle —Equilibrium of immersed and floating
bodies — Densities of solid and liquid bodies ; Areometers.

~T7\ VERY BODY knows that when we immerse in water a sub-
-i-^ stance lighter than itself, — a piece of wood, or cork, for
instance, — it requires a certain effort to keep it there. If left to
itself, it rises vertically and comes to the surface, where it floats,
partly in and partly out of the water.

What is the cause of this well-known phenomenon ? The force
of gravity. In the air, the same body left in the air falls vertically ;
in water, the lateral pressures, the downward pressures, and those
in the contrary direction, are partly destroyed, and are reduced to
a pressure which is exerted in a direction contrary to the force of
gravity. We have proved the existence of this pressure in an ex-
periment before described (Fig. 41). It is stated, and experiment
confirms the theory, that this pressure is precisely equal to the
weight of the liquid displaced. The point of application of this
force, which is called the centre of pressure, is the centre of gravity
of the volume of liquid, the place of which is occupied by
the body. The loss of weight of which we speak being greater,
for bodies lighter than water, than the weight of the body itself,
it is evident that it must cause the body to move in a direction
opposite to that which gravity would impose on it; hence the
rising of the piece of wood or cork to the surface of the liquid.
But this k»ss occurs also in the case of bodies heavier than water,
and in any kind of liquid. Every one knows that it was Archi-

PHYSICAL PHENOMENA.

[BOOK r.

medes, one of the greatest geometers and physicists of antiquity,
who had the glory of discovering this principle, which is known by
his name : —

All bodies immersed in a liquid suffer a loss of weight precisely
equal to the weight of the displaced liquid.

The experimental demonstration of the principle of Archimedes
is made by means of the hydrostatic balance.

Take a hollow cylinder, the capacity of which is exactly equal to
the volume of a solid cylinder, so that the latter can exactly fill the

FIG. 49. — Experimental demonstration of the principle of Archimedes

former. Both are furnished with hooks, so that the solid cylinder can
be placed, with the hollow one above it, below one of the pans of the
hydrostatic balance (Fig. 49). This done, the beam is raised by
means of rackwork fitted to the column of the balance, high enough
to permit a vessel filled with water to be placed beneath the two
cylinders, when the beam is horizontal.

In this state, equilibrium is established by the aid of a counter-
poise in the other scale. If then the beam of the balance is lowered,

CHAP. VH.]

EQCJILIBRIUM OF BODIES IN LIQUIDS.

the solid cylinder is immersed in the water, and equilibrium is dis-
turbed; This alone would suffice to demonstrate the vertical pressure,
or the loss of weight of the immersed body. To measure this weight,
the solid cylinder itself is placed entirely in the water, and equili-
brium is re-established by pouring water slowly into the hollow
cylindrical vessel. It will then be seen that the beam will again
become horizontal, as soon as the hollow cylinder is quite filled.

Thus the loss of weight is exactly equal to the weight of the
water poured in, that is to
say, the water displaced by
the immersed body. The
preceding experiment then
fully proves the principle
of Archimedes.

How is it then that equi-
librium is not disturbed,
when, after having exactly
balanced a vessel contain-
ing liquid and a solid body
placed side by side on the
plate of a balance, the solid
body is immersed in the
water ? The solid body loses
weight, as has been proved.
Nevertheless the equilibrium
remains. It must be that
the vessel and its contents
have been increased by an
equivalent weight, or that,
to put it another way, the

water undergoes from above

FIG. 50.— Principle of Archimedes. Reaction of one immersed

body on the liquid which contains it.

downwards a pressure equal

to that at work upwards. That this explanation is correct is proved

by the aid of the apparatus above described.

A vessel partly filled with water is weighed. Then the solid cylinder
is immersed, supported separately, as is shown in Fig. 50. Equili-
brium is disturbed : the beam leans to -the side of the vessel. By
how much is the weight of the water augmented by the immersion ?

<; 2

76 PHYSICAL PHENOMENA. [BOOK i.

Precisely by the weight of the displaced water : as is proved by the
fact that, in order to again establish equilibrium, it is sufficient to take
from the vessel a volume of water exactly sufficient to fill the hollow
cylinder of the same interior capacity as the body immersed.

The principle of Afchimedes is of great importance. It enables us
to determine the conditions of equilibrium with immersed or floating
bodies, to explain numerous hydrostatic phenomena, and to solve a host
of problems of great practical interest. For example, it enables us to
determine beforehand what must be the forni3 weight, and distribution
of the cargo of ships, in order that stable equilibrium be properly
combined with the other qualities of the vessel, such as rapidity, &c.
At every point we have> in the phenomena which take place in
liquids, proofs of the existence of pressure. When we take a bath, if
we compare the effort which is necessary to raise one of our limbs to
the top of the water with that which it requires in air, we are struck
with the difference. Very heavy stones, that we should have great
trouble to lift out of Water, are moved and lifted with facility when
they are immersed in it. Lastly, when we walk into a river1 which
imperceptibly gets deeper, we feel the pressure of our feet on the
bottom diminish by degreeSj until at last we no longer have any
power to walk forward. The weight of our body is nearly Counter-
balanced by the pressure of the liquid, and we tend to take a
horizontal position in consequence of the unstable equilibrium in
which we find ourselves.

This brings us to say a few words on the conditions of equilibrium
of bodies immersed in liquids or capable of floating on their surface.

It is at once evident that an immersed body cannot be in equili-
brium if its weight exceeds that of an equal volume of the liquid.
In this case it falls, under the action of the excess of weight over
pressure. Neither will it remain in equilibrium if its weight is less
than the displaced liquid: in this case it will rise to the surface,
urged by the excess of pressure over its weight or over the force
of gravity. It is thus that cork, wood — at least certain kinds of
wood — wax, and ice, swim on the surface of water, whilst stones,
most of the metals, and numerous other substances fall to the bottom.
Since mercury is a liquid of great density, most of the metals float
on its surface. A leaden ball, a piece of iron, or copper, will not sink
in it ; gold and platinum will."

CHAP. vil.J EQUILIBRIUM OF BODIES IN LIQUIDS. 77

We shall now examine the case of a body the specific gravity of
which is precisely equal to that of the liquid. If its substance is
perfectly homogeneous, the body will remain in equilibrium, in
whatever position it is placed, in the middle of the liquid. In this
case, the weight and the pressure not only are equal and opposite,
but are both applied at the same point ; that is to say, the centre of
gravity and the centre of pressure coincide.

Fish rise and fall, at will, in water. These different movements
are rendered possible by the faculty these creatures have of com-
pressing or expanding a sort of elastic bag filled With air, situated in
the abdomen. According to the volume of the swimming-bladder —
the name of the organ in question — the body of the fish is sometimes
lighter and sometimes heavier than the volume of Water which
it displaces : in the first case it rises, in the second it descends.
M. Delaunay quotes, in his Course of Physics, a very curious phe-
nomenon which is very easily explained by the principle of Archi-
medes. " When," he says, " a grape is introduced into a glass full
of champagne, it immediately falls to the bottom. But the carbonic
acid, which continually escapes from the liquid, soon forms many
little bubbles rolind it. These bubbles of gas add, so to speak,
to the bulk of the grape, increase its volume, without its weight
being sensibly augmented : the pressure of the liquid which was
at first less than the weight of the grape, soon becomes greater
than this weight, and the grape rises to the surface of the liquid.
If, then, We give a little jerk to the grape, and detach from it the
bubbles of Carbonic acid which adhere to its surface, it again de-
scends to the bottom of the glass, after a short time to remount.
The experiment may thus be continued as long as any carbonic
acid escapes."

If the immersed body is not homogeneous, — if, for example, it is
made of cork and lead, the substances having been combined in such
a manner as to weigh together as much as the displaced water
(Fig. 51), without having a common centre of gravity, the centre
of gravity of the whole and the centre of presswe no longer
coincide. To establish equilibrium these two points must be in
the same vertical plane, as in the positions 1 and 2, or otherwise
equilibrium will be unstable, if, as in 2, the centre of gravity is
uppermost. In position 3, this condition not being realized, equili-

PHYSICAL PHENOMENA.

[BOOK i.

brium will only take place when the oscillations of the body bring
it to the first position.

When a body displaces a volume of liquid, the weight of which
is greater than its own, either in consequence of its real volume
or of its form, it floats on the surface.

In this case, the weight of the water which the portion immersed
displaces is precisely that of the body and the load which it
supports : thus a ship with its cargo of men, materials, and mer-
chandise, weighs altogether just as much as the volume of the
sea^water displaced.

Moreover, the second condition of equilibrium is still the same ; that
is to say, the centre of gravity of the body and the centre. of pressure
must be on the same vertical line. But it is no longer indispensable to
stability that the first point be below the other. Besides, according

FIG. 51. — Equilibrium of a body immersed in a liquid of the same density as its own.

to the position and the form of the floating body, the form of the
displaced volume itself changes, and the centre of pressure changes
with it, so that at each instant the conditions of equilibrium vary.

In ships, perfect equilibrium never exactly exists, even when the
sea is smooth and calm. Oscillations of greater or lesser amplitude
are always taking place ; the principal point to attain is that, under
the most unfavourable circumstances, the movements of the vessel
shall not be decided enough to upset it.

The principle of Archimedes is of the greatest use in science, in
determining the specific gravity of liquid or solid bodies. Let us
briefly indicate the methods adopted for this purpose.

CHAP. VII.]

EQUILIBRIUM OF BODIES IN LIQUIDS.

Let us remember that the specific gravity of a body is the rela-
tion which exists between its weight and that of an equal volume of
pure water taken at a temperature of 4 degrees centigrade. How can
we find the number which expresses the specific gravity of a body ?
First, we must obtain its weight : for this the balance is used. Secondly,
we must know the weight of an equal volume of water: the opera-
tions necessary for this determination will be described in the sequel.
These two numbers obtained, the quotient, the first divided by the
second, gives the specific gravity.

The only difficulty is then to find the weight of a volume of water
equal to that of the body. We
shall explain the three methods
employed. Let us take the case
of a piece of iron weighing in
the air 246 '5 gr. It is sus-
pended by a very fine cord to
one of the plates of the hydro-
static balance, and to establish
equilibrium a counterpoise is
placed in the other plate. Then
the balance is lowered until the
piece of iron is immersed in
the water (Fig. 52). At this
moment the beam falls on the
side of the tare, and it is
necessary to put weights equal
to 31*65 gr. in the plate which
holds the body, to re-establish
equilibrium. These weights re-
present the displaced water. On
dividing 246'5 by 31-65, 7'788
is found to be the specific
gravity of the iron, which shows

that for equal volumes the iron weighs 7 and 788 thousandths times
as much as water. We now come to the second method.

Fig. 53 represents an instrument called an areometer,1 which was

Fia. 52.— Dcusii> of solid bodies. Mettiod of the
hydrostatic balance.

1 From the Greek apaios, right, and pfrpov, measure. Areometers were first
used to determine the densities of liquids.

SO-

PHYSICAL PHENOMENA.

[BOOK i.

invented by the physicist Charles, although it is generally attributed
to Nicholson ; it is constructed so that when placed in water the
liquid is precisely level with a standard point on its upper rod, when
the pan which surmounts this rod is charged with a known weight,
let us say 100 grammes. We place the body whose specific gravity
is sought for in the little pan at the top, and standard weights
are added to obtain the level If, for instance, 35'8 gr. have been
added, the difference, 64'2 gr., of this last weight and the 100 grammes
evidently gives the weight of the body in air.

From what has been said it will be seen that the areometer is a
true balance.

Fio 53.— Densit. of solid holies. Arooir.cter of Charles or Nicholecu.

The body is next taken out of the upper pan, and is placed in the
little vessel suspended under the instrument : it loses some of its
weight, so that the areometer rises, and more standard weights must
be added to bring it again to the level : let us suppose 31 grammes
added — this is the weight of a volume of water equal to that of the
body. Dividing 64'2 by 31, we find 2'07 the ratio sought (the
specific gravity of sulphur).

CHAP. VII.]

EQUILIBRIUM OF BODIES IN LIQUIDS.

In the case where the body is lighter than water, the small basket
is reversed over it, and the body, which pressure causes to rise^
meeting with an obstacle, still remains immersed.

A third method to determine the specific gravities of bodies is that
of the "specific gravity bottle." Placed in the pan of a balance is
the fragment of a body the weight of which is known, but of which
the specific gravity is sought, and, by its side, a flask exactly filled
with water and well stopped by means of a ground stopper (Fig. 54).
Equilibrium is obtained by standard weights. The body is then

Fio. 54.— Density nf solid
bodies. Method of the
specific gravity bottle.

FIG. 55.— Density of liquids. Hydrostatic balance.

introduced into the flask, which is again stopped, care having been
taken to push the stopper to the same level. A certain quantity
of water has come out, the volume of which is precisely equal to
that of the body which takes its place. After having well dried
the flask, it is replaced in the pan of the balance, and the weights
required to restore equilibrium give the weight of the water expelled.
Having the weights of equal volumes of the substance and of water

PHYSICAL PHENOMENA.

[BOOK i.

its specific gravity is easily determined. This process is not an
application of the principle of Archimedes, like the first two.

These three methods require some precautions ; the body im-
mersed in the water retains, adhering to its surface, air-bubbles which
must be removed. If the body easily absorbs water, or even dis-
solves in it, another liquid is used — oil, for example — in which case
we must determine the density of the body relatively to the oil, that
of the oil being known, or determined as below.

The specific gravity of liquids is determined by processes
analogous to those we have just described. A hollow glass ball,
ballasted so that it is heavier than the liquids to be weighed, is
hooked under the pan of the hydrostatic balance (Fig. 55).

FIG. 56 — Specific gravity of liquids. Fahrenheit's

Areometer.

FIG. 57. — Specific gravity of liquids.
Method of the specific gravity
bottle.

Weigh it in air and then in water, the difference of the weights
gives the weight of a volume of water equal to its own. Dry it well,
and weigh it in the liquid of which the specific gravity is wanted,
the difference between this weight and that in air gives the weight of
an equal volume of the liquid. Dividing the latter weight by the
former, the quotient is the specific gravity sought. Fahrenheit's areo-
meter (Fig. 56), immersed in water, requires a given weight to be

CHAP. VII.]

EQUILIBRIUM OF BODIES IN LIQUIDS.

placed on it, so that a fixed standard point on its rod is level with the
surface of the liquid. It is clear that this additional weight, together
with that of the instrument, marks the weight of the volume of water
displaced. Immersed in another liquid, in oil for example, we obtain
in the same way the weight of a volume of oil equal to the volume of
the body. The division of the second weight by the first gives the
specific gravity of the oil. Lastly, with a flask terminated by a
straight tube (Fig. 57), which is successively filled with water and
some other liquid as far as the standard mark on the stem, the weights
of the two equal volumes of water and of the liquid are found, and
thence the specific gravity.

To terminate this chapter, we give a table of the specific gravities
of some of the most common solids and liquids. As we shall
soon see, the volumes of the bodies vary according to the degree of
temperature at which they are determined. These variations do
not affect their weight, but precisely on that account the specific
gravity of the body is variable. It has therefore been necessary to
reduce them to a constant temperature. For water only, this tem-
perature is 4° C. ; for all the other solid and liquid substances, it is
convenient to take that of melting ice, or 0° C.

SPECIFIC GRAVITIES OF DIFFERENT BODIES AT 0° C.

SOLIDS.

Metals.

Rolled platinum . 22'06
Cast gold . . . 19-26
Cast lead . . .11-35
Cast silver . . . 10 '47

Minerals,
Diamond
Marble .
Granite .
Sandstone

Rocks, &c.

. . . 3-53
. 2-65 to 2'84
. . . 2-75
. . . 2'60

Vegetables, &c.
Boxwood . . .
Heart of oak . .
Black ebony . .
Oak

1-32
1-17
1-19
0'91

Drawn copper wire '8'95
Cast ditto . . . 8'85
Iron 7-79
Tin 7 "29

Quartz .
Glass .
Porcelain
Sulphur

. . . 2;65
. . . 2-50
. . . 2-24
. 2 08

Beech ....
Willow ....
Poplar ....
Cork

0-75
0-49
0-39
0-24

Aluminium . . 2'67

Ice at 0°.

. . . 0'93

Elder pith . . .

0-08

LIQUIDS.

Mercury . . . 13-596
Bromine . . . 2'966
Concentrated sul-
phuric acid . 1*841
Nitric acid . . 1'520
Water at 4° . I'OOO

Water at 0° .

. 0-9998

Olive oil . . . 0-915

Sea-water .

. 1-026

Essence of turpen-

Milk . . .

. 1-03

tine .... 0*865

Bordeaux. .

. 0-994

Alcohol. . . . 0-792

Burgundy .

. 0-921

Sulphuric ether . 0'736

H 2

84 PHYSICAL PHENOMENA. [BOOK i.

CHAPTER VIII.

WEIGHT OF THE AIK AND OF GASES. — THE BAROMETER.

WE live at the bottom of a fluid ocean, which envelopes all
portions of the terrestrial spheroid, and of which the mean depth
is at least a hundred times greater than that of the seas. The
substance of which this ocean is formed is the air, a mixture of
various other gases, the two principal being oxygen and nitrogen.
Carbonic acid gas, aqueous vapour, sometimes ammonia, are also
found, but in variable proportions, whilst the two gases first named
are everywhere found in the same proportion — a proportion such
that, by volume in 100 parts, 21 are oxygen and 79 nitrogen.

Air is, as is well-known, the indispensable aliment to the respira-
tion of animals. Those even which habitually live in water cannot
do without it. It is not less necessary to the vegetable world, which,
under the influence of light, decomposes the carbonic acid in the air,
fixes the carbon and liberates the oxygen, which, in its turn, is
absorbed in animal respiration.

The transparency of the air itself is so great that we cannot see it,
at least when we are dealing with a stratum of small thickness. In
the case of great distances the effect of the interposition of gaseous
strata is very perceptible ; it gives to distant bodies, such for
example as mountains bounding the horizon, a bluish tint, and
this tint, very brilliant and pure, forms the colour of the sky

CHAP, vni.] WEIGHT OF THE AIR AND OF GASES. 85

when the .atmosphere is cloudless. Were it not for the blue colour
of the atmosphere, the sky would be colourless, that is, entirely
black; and the stars would then stand out brightly in broad day.
During the night, the aerial envelope, being no longer lighted up by
the rays of the sun, but only by the feeble light of the moon and stars,
appears of a dark blue ; and, if in the day we observe it from a very
high mountain, the same appearance is produced — the thinner stratum
of the air above us, which moreover is less dense in the higher regions,
absorbing but a slight portion of the blue rays of the solar light.

The existence of air is revealed to us by other phenomena,
which act upon us through the medium of the organs of hear-
ing and touch. When the air is still, it is only necessary for us to
move in order to feel its presence. The mass of air resists the dis-
placement which we cause in it, and the resistance is sensible to our
hands or our face. But the material nature of the air is manifested
still more perceptibly by the movements with which it is itself
animated ; from the lightest breeze to the most violent winds,
hurricanes, and tempests, all atmospheric agitations are continual
proofs of its existence.

Lastly, it is in consequence of the vibrations communicated to
the air by sonorous bodies that sound is propagated to our ear. The
air itself, when it is put in vibration under favourable conditions,
becomes a producer of sound, as we shall see further on. Most of the
properties of air have been utilized, and we shall, in the sequel,
describe numerous and very interesting applications. The object of
this chapter, meanwhile, is the study of the properties of air con-
sidered as a body which has weight, and of those phenomena due to
the weight of air or other gaseous substances. That air has weight
is easily proved by a very simple experiment.

We shall shortly describe the instrument which is used to ex-
haust the air which it contains from a vessel or receiver — to make a
vacuum, as physicists say. This is called an air-pump. If we
take a hollow glass tube fitted with a metallic neck furnished with a
stopcock, and weigh it after having made a vacuum (Fig. 58), we
have only to open the cock and allow the air to enter, to see that
the beam of the balance leans towards the side of the ball. To re-
establish the interrupted equilibrium, weight must be added — about
1*29 grammes for each litre that the globe holds.

PHYSICAL PHENOMENA.

[BOOK i.

Thus then is the weight of the air directly demonstrated. The
same experiment, made with other gases, proves in the same manner

that bodies in a gaseous state,
like liquids and solids, obey the
action of gravity. Galileo first sus-
pected and enunciated the import-
ant truth that air is heavy; but
the experiment we have just indi-
cated is due to Otto de Guericke,
the inventor of the air-pump.

If the air contained in a vessel
is heavy, that is, if its weight is
susceptible of being valued by
means of a balance, the immense
volume of air which rests on the
surface of the earth must press on
it in proportion to its mass, and
this pressure, which is doubtless
enormous, must be manifested in
some way. This is indeed what
happens ; but before studying these
phenomena, let us say a few words
on the properties of gases, both

those which they possess in common with liquids, and those which
characterize them in a special manner.

Like liquids, gases are formed of particles — molecules — which
glide one over the other with extreme facility. Thus we see gaseoiis
masses give way to the least force — dividing themselves, and allow-
ing all the movements of solid and liquid bodies to continue
in their midst, and not opposing them with sensible resistance,
until the velocity and displacement of their molecules become
considerable. ;" :

Gases are eminently elastic and expansible. Let us take a
flattened and compressed bladder, only inclosing a small volume of
air in comparison with the quantity which the same bladder when
filled out would hold (Fig. 59). In this state, the interior air does not
increase in volume, because the elastic force with which its molecules
fire endowed, and which we are about to demonstrate, is balanced by

FIG. 58.— Experimental demonstration of the
weight of air and other gases.

CHAP; vin.] WEIGHT OF THE AIR AND OF GASES. 87

the pressure of the exterior air. Let us place this bladder under the
receiver of an air-pump. In proportion as the vacuum point is
approached, we shall see the bladder increase in volume ; it swells
out, and may burst under the interior pressure which distends its
walls. Let the air again into the receiver — it immediately returns
to its primitive volume; which at once proves that air — and any
other gas would conduct itself in the same manner — is elastic and
compressible.

FIG. 59.— Elasticity and compressibility of gases.

These two properties are also proved by the aid of the fire-syringe.
In forcing a well-fitted and greased piston into a glass tube filled
with air (Fig. 60), we experience a slight but increasing resistance,
and the volume of the air diminishes one-half, two-thirds, &c. This
first operation proves the great compressibility of gases. When the
piston has arrived at the end of its course and is abandoned to
itself, it returns spontaneously to its original position— a proof no
less evident of the elasticity of the air.

As compression produces heat, this apparatus may be used to
light a piece of tinder placed under the piston ; but in this case the
compression* must be very rapid. Hence the name given to the in-
strument. Gases then, like liquids, are elastic and compressible ; but
whilst this latter property is very slight in liquids, it is, on the
contrary, very marked in the case of gases. We may also notice
that if liquid molecules have a cohesion nearly nil, in gases the

PHYSICAL PHENOMENA.

[BOOK T.

molecules have a tendency to repel each other, which is only counter-
balanced by pressure from without. Hence it follows that when
this pressure diminishes, the volume of the gas increases ; in liquids

the volume remains constant, at least as
long as the body retains the same state.

One last property which distinguishes
liquids from gases, is the very feeble
comparative density of the latter.
Whilst the weight of a litre of liquid
may be as high as 13596 grammes (the
weight of a litre of mercury), and is never
lower than 715 grammes (ether), the
weight of a litre of gas or vapour never
exceeds 20 grammes and may be as low
as 9 centigrammes. Moreover, in gases
as in liquids, the principles of equality of
pressure and of equality of transmission
of pressure in every direction, are indi-
cated by theory and verified by experi-
ment ; we shall have occasion soon to
give some examples of this. Let us
now return to the phenomena due to the

FIG. 60. — Pneumatic syringe.

weight of the air.

We have seen that Galileo was the first who suspected that the air
has weight. The history of the discovery is well known. It was made
in 1640. Some Florentine workmen, ordered to construct a pump in
the palace of the Grand Duke, were greatly astonished that, in spite
of the good condition into which they had put the mechanism, the
water would not rise to the upper extremity of the pipe of the body
of the pump, that is to say, beyond 32 Roman feet (about 10'3m.).
The learned men — engineers and Florentine academicians — who were
consulted on this anomaly, did not know what to answer. They
addressed themselves to Galileo, then aged seventy-six 'years, whose
immense reputation had not been shaken by persecutions. Galileo at
first gave an evasive answer, but the question made hjm reflect. He
saw at last that the pressure of the air must be the cause which made
the water rise to this precise height, and that " Nature's abhorrence of

CHAP, viir.] WEIGHT OF THE AIR AND OF GASES. 89

a vacuum "was an idle explanation, as it required us to suppose
that this abhorrence would not manifest itself beyond a given height.
He proved the weight of the air by weighing a bottle, before and after
the air had been expelled by the vapour caused by the ebullition of
a certain quantity of water. But he left to his disciple Torricelli the
care of extending the verification of his conjectures.

A year after the death of Galileo, it occurred to Torricelli to
examine how mercury, a liquid denser than water, would act in
vacuo.

He took a long tube closed at one end, which he filled with this
liquid; then, covering the open end of the tube with his finger, in
such a way as to prevent the liquid from falling out and the air from
getting in, he plunged this extremity into a vessel full of mercury.
Leaving the liquid to itself, he then held the tube in a vertical
position (Figs. 61 and 62). Torricelli saw the liquid descend from
the top, and after a few oscillations, settle itself at a level which
remained nearly invariable at 28 Eoman inches (29'92 English inches
or 76 centimetres) above the level of the mercury in the vessel.

If Galileo's idea was right, if the column of water of 32 feet
was really maintained by the pressure of the atmosphere, the same
pressure would raise the mercury, being thirteen times and a half
heavier than water, to a height thirteen times and a half less. Now,
28 inches are thirteen and a half times less than 32 feet !

Such, in its simplicity, is this grand discovery. Such is Torricelli 's
tube, or, as it is now called, the barometer, an instrument used to
measure the pressure of the atmosphere. It was not without oppo-
sition that the explanation of Torricelli on the elevation of water and
mercury was accepted by the scientific men of his day. But addi-
tional experiments suggested by Pascal left no doubt. Pascal
remarked that if the weight of the air were really the cause of the
observed phenomena, the pressure ought to be less in proportion as
the barometer was observed at a greater height in the atmosphere, since
the gaseous column superposed above the exterior liquid would be
less. The height of the mercury in Torricelli's tube ought then to be
smaller at the top of a mountain than in the plain. Hence the
famous experiments which he made with Perier, his brother-in-law,
on the Puy-de-D6me, and those which he executed himself at the
base and at the top of the tower of Jacques la Boucherie. The

PHYSICAL PHENOMENA.

[BOOK i.

results were in every point conformable to the inferences drawn from
the new theory.1

The height of the mercury in Torricelli's tube is independent of
its diameter, provided always that this diameter be not too small :

FIG. 61.— Torricelli's experiment.

PIG. 62. — Tonicelli's experiment. Effect of the
weight of the atmosphere.

for then other forces which we shall study subsequently have a great
influence on the level of the liquid. This fact is a very natural

1 " I have thought," wrote Pascal to Pe"rier, " of an experiment which will
remove all doubt, if it be executed with exactness. The experiment should be made
in vacuo several times, in one day, with the same quicksilver, at the bottom and
at the top of the mountain of Puy, which is near our town of Clermont. If, as I
anticipate, the height of the quicksilver be less at top than at the base, it will
follow that the weight or pressure of the air is the cause of this ; there certainly
is more air to press at the foot of the mountain than at its summit, while one
cannot say that Nature abhors a vacuum in one place more than in another."

CHAP, viii.] WEIGHT OF THE AIR AND OF GASES. 91

consequence of the equal transmission of pressure in liquids: the
column of mercury acts by its weight on all the mercury in the
trough, so that each element of surface equal to the section of the
tube is pressed equally by this weight. And as there is equili-
brium, it follows that the pressure of air on this same unit of
surface is precisely equal to the pressure of the mercury.

What must we conclude from this ? That the mass of the
atmosphere presses on the earth's surface, as if this surface were
everywhere covered with a stratum of mercury about 76 centimetres
thick. Let us add, that the pressure in the air being transmitted
equally and in every direction, the weight of the atmosphere makes
itself felt wherever the air penetrates and by whatever remains
in communication with it, as in the interior of houses, in cavities
and on the surface of bodies. This explains why all bodies situated
on the earth's surface are not crushed by this enormous pressure,
which is not less than 10,333 kilogrammes (about 10 tons) on the
average on each square metre of surface. The surface of the human
body being nearly a square metre and a half for a person of average
height and size, each of us always supports a load which is about
equal to 15,500 kilogrammes (nearly 1 5 tons). We have just given the
reason why this load does not crush us : all the pressures exercised
on every part of our body and from within produce equilibrium.

At first sight it seems incomprehensible that we should not be
ground to dust under the effect of these contrary pressures. The reason
is very simple. All the fluids contained in our organism act against
the pressure of the atmosphere, and it is this constant reaction which
explains our insensibility to pressure, and the absence of the pheno-
mena which the pressure of the air seems, at first, certain to cause.
This reaction is not a simple hypothesis, as the process of " cupping "
proves. " Cups " are small vessels of metal or glass, which are applied
to the skin: a vacuum being made inside them, the skin swells up,
the small veins burst, and the blood flows out, because it is no
longer maintained in the veins by atmospheric pressure.

In ordinary courses of physics, some interesting experiments
are introduced to show the energy of atmospheric pressure. These
we will rapidly describe.

One of the first known is that of the Magdeburg hemispheres :
it is attributed to Otto de Guericke.

92 PHYSICAL PHENOMENA. [BOOK i.

Two copper hemispheres fitting one on to the other, in such a way
as to form a hollow sphere, are fixed by a stopcock to the pipe of the
air-pump (Fig. 63). While they are full of air, the slightest effort is
sufficient to separate them. But when a vacuum is made in the
interior of the sphere, it requires a considerable effort to effect the
separation. This is easy to account for, since the pressure on two
hemispheres of only 2 decimetres (about 8 inches) in diameter, is
324 kilogrammes (about 6 cwts.) on each of them.

In one of his experiments, the illustrious burgomaster of Magde-
burg caused each hemisphere to be pulled by four strong horses
without being able to separate them ; the diameter of the hemispheres
being 65 centimetres (26 inches), the pressure was 3,428 kilogrammes
(about 3J tons). The total pressure on the hemispheres is even
greater ; but we speak only of what is exerted in the direction of

FIG. 63. — Magdeburg hemispheres. FIG. 64.— Bursting a bladder by exhausting

the air beneath it.

resistance, which equals on either side the pressure on a circle of
the same diameter as the sphere.

Another experiment consists in making a vacuum in a vessel, over
the mouth of which a bladder has been stretched, which prevents
the air from getting in. As the vacuum point is approached, the
membrane is depressed under the weight of the exterior air, and
at last it bursts (Fig. 64), a loud detonation similar to that of a
pistol-shot accompanying the rupture. This detonation is evidently
owing to the sudden entrance of the air into the cavity of the

CUAP. VII1.J

WEIGHT OF THE AIR AND OF GASES.

vessel. If an apple is applied to the end of a thin metallic tube,
in the exterior of which a vacuum is made, being pressed by the
weight of the atmosphere, it is cut by the edges of the tube, and
a part penetrates into the interior.

Lastly, there is a curious experiment which demonstrates the
pressure of the air on the surface of liquids. A cylindrical glass bell
jar, mounted on a metallic stand, is furnished with a tube and stop-
cock, which allows of its being screwed on the air-pump, and a

FIG. (55. — Jet of water in vucuo.

vacuum being made in its interior. When the vacuum is made, the
lower end of the tube is immersed in a basin filled with water, and
the tap is turned, which opens the communication between the
interior of the vessel and the liquid. The atmospheric pressure
which is exerted on the water in the basin causes a jet which
strikes the top of the bell jar (Fig. 65).

In what has preceded, we have supposed that the weight of the
column of air was the only cause of the atmospheric pressure ; that
this pressure was constant ; and that it was equivalent, on a given

94 PHYSICAL PHENOMENA. [BOOK i.

surface, to the weight of a column of water of 32 feet, or 10*33
metres, or to that of a column of mercury of 29*92 inches, or 76 centi-
metres, having the same sectional area. But experiment proves that
this pressure is subject to variations, even in the same place.
Further on, we shall study these variations in their relation to
meteorological phenomena ; but for this purpose we must possess an
instrument which indicates them. This instrument, which in prin-
ciple is no other than Torricelli's tube, and which is called a
barometer, deserves a detailed description. It has been differently
arranged according to the use to which it is destined, and with
the object of rendering its indications precise.

The most simple and at the same time the most exact barometer
is nothing more than a tube of glass, which is chosen straight,
regularly cylindrical and perfectly homogeneous, of a diameter about
three-quarters of an inch, or 2 or 3 centimetres. It is immersed,
after having been filled with mercury, in a trough filled with the
same liquid.

The trough and the tube are fixed against a vertical support, and
remain in the place where the observations are to be made. It
is nothing more, as is seen, than a Torricelli's tube. But properly to
arrange it, various precautions must be taken, the importance of
which is very obvious, and which are equally necessary for the
construction of other barometers.

Thus, it is essential that the mercury used be of great purity.
This is arrived at by acting upon oxide of mercury with nitric acid ;
and great care must especially be taken that it does not contain
air-bubbles, as their lightness would cause them to rise along the
sides of the tube into the vacuum, which is called the Torricellian
vacuum. Aqueous vapour and air, being elastic gases, would press
the upper level of the mercury, so that its height would not indicate
truly the pressure of the atmosphere. To effect this, the tube must
be dried and perfectly cleaned before filling it. Once the tube is
filled with mercury, the liquid is boiled in it over burning charcoal,
until all the air-bubbles it contains are expelled. At this moment the
aspect of the mercury should resemble a bright mirror; the bright
and metallic lustre with which it shines indicating the perfect purity
which is indispensable for our purpose.

The large diameter of the tube which forms the standard or

CHAP. VIII.]

WEIGHT OF THE AIR AND OF GASES.

.95

normal barometer possesses this advantage over smaller ones,
that it gives a level to the mercurial column which is not altered
by the molecular force called capillarity. In this instrument, in
order to obtain the height of the barometer, it is sufficient to
measure the vertical distance
which separates the upper level
from that of the mercury in
the trough. This is done with
a special instrument called a
cathetometer, which is com-
posed essentially of a divided
vertical scale on which a glass
vernier moves.

There may be seen on
Fig. 66, which represents a
standard barometer, a double
screw fixed to the trough.
The lower end should be on a
level with the mercury, which
is easily accomplished by
means of the screw, and it is
the distance from the upper
point of this screw — which
the draughtsman has forgotten
to figure — to the upper level
of the mercury in the tube
which the cathetometer gives.
By adding to it the constant
length of the screw, we have
the height, or the atmospheric
pressure sought for.

The cistern barometer is dis-
tinguished from the preceding
one by having a glass cistern

into which the tube is inserted (Fig. 67) ; possessing a large surface,
the level of the mercury in it may be considered as constant.
The stand on which the instrument is fixed is furnished with a
graduated scale, on which slides a movable index placed in such

FIG. 66.— Normal or
standard barometer.

Fir,, 67. — An ordinary
cistern barometer.

PHYSICAL PHENOMENA.

[BOOK i.

a way that its lower edge is on a level with the surface of the
mercury. The zero of the scale being by hypothesis the level of
the mercury in the cistern, the reading of the height is made at
once on the scale. Lastly, the scale is furnished with a vernier,
which gives the fractious of millimetres or inches. The arrangement
which renders this instrument less perfect than
the preceding, is that the level of the cistern or
the zero of the scale is supposed to be constant ;
whereas under the influence of the variations of
temperature the glass and the mercury expand,
and this produces variations in the position of
the zero point. Frequently, after a time, these
accidental variations produce a permanent altera-
tion, and the scale has to be slightly rectified.

The barometers suggested by Fortin, Gay-Lussac,
and Bunten are not liable to these inconveniences.
But as they are principally constructed with the
object of being easily transported, the diameter
of the tube is smaller than in a standard baro-
meter, so that capillarity depresses the upper
level of the mercury. The observations made
with these instruments require therefore a cor-
rection to free the readings from this error.
But in Gay-Lussac's barometers arid those
of Bunten, as in the standard barometer, the
height is measured by two corresponding
scales at the two levels of the liquid, so that
the difference, with all corrections made, gives
the real atmospheric pressure. In that of Fortin,
the zero point is maintained constant by an
ingenious contrivance which will be easily com-
prehended from Fig. 68.
We have a section of the cylindrical cistern which incloses the
mercury in which the slender part of the tube is immersed. The
upper part of the cylinder is of glass, and shows the level of the-
liquid. A metallic point in the interior indicates the position of
the zero of the scale and the level the mercury ought to attain
every time an observation has to be made. As the mercury rests

Fie. 68.-- Cistern of Fortiu's
barometer.

CHAP. VIII.]

WEIGHT OF THE AIR AND OF GASES.

on a bag of impermeable leather connected with the lower walls of
the cistern, and as the metallic base is traversed by a screw, the
end of which presses against the elastic bag, it follows that we can
at will raise or depress the bottom of the liquid, or, what is the

FIG. 69. — Fortiii's barometer, as arranged for travelling.

same thing, raise or depress its surface, and thus obtain the level
required. For travelling, in order that the movements of the heavy
fluid may not break the tube the screw is raised, until the cistern

PHYSICAL PHENOMENA.

[BOOK i.

is entirely full in its upper part. As all the apparatus is inclosed
in a brass cylinder, which preserves it from shocks, the level of
the mercury of the tube is observed through two longitudinal
apertures on opposite sides, which enables us to view the glass
tube ; on the edges of these apertures the divisions, in inches or
millimetres, of the scale, which has its zero at the constant
level determined by the position of the cistern, are
engraved. An index, furnished with a vernier and a
milled head, which enables it to be moved by the aid of a
rack and pinion, gives the precise position of the level on
the scale, and the height in hundredths of millimetres or
inches. The apparatus is supported by a tripod resting
on the ground, and care must always be taken to place
the tube in a vertical position, which is rendered easy by
its mode of suspension.

Fortin's barometer is convenient for scientific explora-
tions, because the air cannot enter, and the movements
and joltings inseparable from travelling cannot break it.
The readings require to be corrected for the effect of
capillarity. Moreover, as temperature causes the density
of liquids to vary, a correction must also be made to
eliminate this source of error.

Fig. 70 shows the arrangement of Gay-Lussac's baro-
meter as modified by Bunten. Two portions of the same
tube are united by a very narrow or capillary one. A
small opening allows the air to penetrate above the lower

Fio.70. — Gay-
barometer, level. The barometric height is measured on a scale

Suntend by divided in millimetres or inches, the height of the upper
level being taken, and the height of the lower level being
subtracted from it ; the difference evidently giving the pressure. As
the tubes have the same diameter, Gay-Lussac thought it would be
unnecessary to correct for the influence of capillarity ; unfortunately,
however, it has been found that this influence is not the same in
the barometric vacuum and in the lower tube. This is unfortunate,
as the instrument is easy to transport, it is not large, and the air can
only with difficulty penetrate the barometric chamber, on account
of the slight diameter of the intermediate tube. In travelling it
is inverted. The modification designed by Bunten renders the

CHAP. VIII.]

WEIGHT OF THE AIR AND OF GASES.

introduction of air still more difficult, since if the bubbles penetrate
along the walls of the tube, they lodge themselves in the narrow
space in the widest part of the capillary tube, and have no action
on the level of the mercury.

Some of our readers will perhaps be anxious to know by what
means the variations of the atmospheric pressure can be indicated

FIG. 71.— Dial or wheel barometer.

by a movable needle on a graduated dial. The dial or wheel
barometers, to which we allude, are not of great scientific value,
because they are rarely constructed with sufficient precision ; they
are used in rooms as ornamental objects. The dial-barometer is
composed of a siphon tube, the open branch of which (Fig. 71)
supports an ivory float. This float rises and falls, and by its motion
turns, by means of a silken thread, a pulley, on the axle of which

I 2

100 PHYSICAL PHENOMENA. [BOOK i.

the needle is fixed. The needle turns in either direction, according
as the surface of the liquid rises or falls ; the dial is divided by
comparing it with a fixed barometer. We shall see, further on, what
is signified by the weather indications which we are accustomed to
see written against the different divisions of the dial.

For many years metallic or aneroid barometers have been
substituted with advantage for these instruments, the indications
of which are only of inferior precision. These are based on the
elasticity and the flexion of metals formed into thin plates. A
flattened brass tube, the section of which is elliptical, is exhausted
of air and carefully closed (Fig. 72). It is curved in the form

I1 10. 7'2. — Bourdon's aneroid barometer

of an arc of a circle, and fixed at its middle point, so that the
disengaged extremities of the two halves of the tube can oscillate
on either side this fixed point. When the barometric pressure
increases, the pressure flatteos the tube, which effect causes the
curvature of the two arcs to augment, and their free extremities
approach each other; the opposite takes place if the pressure
diminishes. The disengaged extremities of the tube are con-
nected with levers which move the axis of a cogged sector. The
needle of the dial, which is connected by a pinion to this sector,
moves either in one direction or the other, and in this manner
traverses the divisions on the dial, which are engraved by comparison
with a standard barometer.

CHAP. VIII.]

WEIGHT OF THE AIR AND OF GASES.

101

In the aneroid represented in Fig. 73, the pressure of the air is
exerted on the corrugated top of a metallic drum, the interior of
which has been exhausted of air. When the pressure aufments, this
top sinks down ; it rises, on the contrary, if the pressure diminishes,
and its movements are transmitted to a needle by a pecular mecha-
nism, the detailed description of which would here be superfluous.

Fiu. 73. — Vidi's aneroid barometer

The invention of this barometer is due to M. Vidi. It has been
recently perfected by an English optician, Mr. Cooke.

This kind of barometer is preferable to the dial-barometers,
although from time to time it is necessary to modify the graduation
or to apply corrections on account of the variations to which the
molecular state of the tube in the Bourdon barometer, or that of the
metallic box and of the antagonistic spring in Vidi's instrument, is
subject.

102 PHYSICAL PHENOMENA. [BOOK L

CHAPTER IX.

WEIGHT OF THE AIR AND OF GASES (continued}. — PUMPS —

MARIOTTE'S LAW — THE AIR-PUMP.

Principle of the ascent of liquids in pumps— Suction and force pumps— The
siphon — Air-pump ; principle of its construction — Double and single barrel
air-pumps — Condensing pumps — Mariotte's law.

THE discoveries of the weight of the air and of atmospheric
pressure only took place a little more than two centuries ago.
But long before Torricelli and Galileo, the application of the principle
had taken precedence of the theory, as is proved in the account we
have given, as history has handed it down to us. It is, in fact,
the pressure of the air which is the cause of the ascending movement
of water in pumps. Now, the invention of these useful instru-
ments is generally attributed to Ctesibius, a celebrated geometer and
mechanician, who lived at Alexandria 130 B.C., or about a century
after Archimedes.

We shall now briefly describe the different instruments known
under the name of pumps, the object of which is the movement of
liquids and gases, keeping here particularly in view the explanation
of the action of these instruments. We return, in the volume
which treats of the applications of physics, to the detailed description
of those which have a special use in the industrial arts.

Let us take a hollow cylinder, in which a piston furnished with
a rod may be moved up and down, and in the bottom of which an
orifice is made (Fig. 74). The piston having been lowered to the
bottom of the cylinder, the instrument is immersed in a vessel or
reservoir full of water ; then the piston is raised by its rod. What
happens ? The space void of air, which the piston leaves under it

CHAP. IX.]

WEIGHT OF THE AIR AND OF GASES.

103

in its ascending movement, will be filled with water, first until the
level of the water is the same in the cylinder as in the reservoir.
This takes place in virtue of the principle of the equilibrium of
liquids in communicating vessels, so that it would happen even if
there was air under the piston. But the water still rises above this
level, keeping in contact with the piston
the lower surface of which it constantly
touches ; and it is easy to understand that
its movement is due to the pressure which
the outer air exerts on the liquid surface
of the reservoir.

Let us suppose that the cylinder has
an elevation of more than 32 feet : the
liquid column will rise until it attains
about this height. At this moment its
weight is in equilibrium with the pres-
sure of the atmosphere ; if the piston con-
tinues to rise, the water will not follow
it. This is precisely the obstacle which
the Florentine workmen encountered, and
which caused the physicists belonging to
the Court of the Grand Duke to believe
that Nature ceased to abhor a vacuum
beyond 32 feet.

Such is the principle of the pump to which is given the name of
Suction-pump, because the piston appears to suck up the liquid as it
rises. We shall now show how the instrument is generally arranged
when it fulfils the object for which it is intended ; that is, to give
us a supply of water which has been raised to a certain height above
the level of the reservoir.

The cylinder, or body of the pump, is furnished with a cylin-
drical tube of small diameter, the lower extremity of which is placed
in the reservoir. At the junction of the cylinder and tube a valve is
fitted, which opens upwards. The piston itself has one or more open-
ings, furnished with valves, the action of which is in the contrary
direction to the first (Fig. 75). It is easy to see what will happen when
we give an alternating movement to the piston in the body of the
pump. At its first ascent a vacuum is made under it. The air in

FIG. 74.— Principle of the suction-
pump.

104

PHYSICAL PHENOMENA.

[BOOK i.

the suction-tube lifts the valve by its pressure, and the water rises to
a certain height. When the piston again descends, the air which is
introduced into the body of the pump is compressed : on the one hand,
its pressure closes the lower valve, and, on the other, the compressed
air lifts the valves of the piston and escapes upwards. At each stroke
the water rises higher and higher, till it comes in contact with the
lower wall of the piston, and passes through the valves to^its upper
surface. It will be easily seen how the water is forced to flow out
by a lateral orifice at the upper part of the pump. Moreover, once

the pump is in action, when the piston
rises a vacuum is made beneath it, and tiie
water continues to press against its lower
side. The valve of the suction-tube
remains constantly open, and the ascent
of the water is determined by the move-
ment of the piston.

The effort necessary to raise and lower
the piston, when the punip is in action, is
easily measured. If the piston descends,
its own valves are open; the pressures
transmitted to its opposite sides by the
liquid are equal the one to the other, and
consequently are counterbalanced, and the
only resistances felt proceed from the
friction of the liquid and the piston. But
if the piston is raised, the atmospheric
pressure is alone annulled, as it is exerted
on the reservoir on the one hand, and on
the upper level of the liquid on the other.
The effort required is measured by the
weight of a column of water, having

for its base the surface of the piston, and for its height the
vertical distance between the two levels of the liquid. If, for
example, this distance is 2 metres, and the base of the piston is
1 square decimetre, it will require a force of 20 kilogrammes to
raise the piston, without taking into account the resistance due
to friction.

Experiment shows that it is not possible to give to the suction-

FIG. 75.— Suction-pump.

CHAP. IX. ]

WEIGHT OF THE AIR AND OF GASES.

105

pump a depth of more than about 20 feet, instead of 32 feet as
indicated by theory. The reason of this lies in the escape of air and
water which always takes place between the pump itself and the
piston ; besides, the water of the reservoir nearly always contains air
in solution, and this frees itself from the ]iquid whenever it is brought
up to a region of less pressure.

In the Force-pump (Fig. 76) the body of the pump is immersed in
water, so that the liquid is introduced into it by simple communi-
cation. Moreover, the piston is solid, and the tube used to raise the

FIG. 76.— Force-pump.

FIG. 77.— Combined suction and
force-pump.

water, starting from the lower part of the pump, is furnished at the
point of junction with a valve which opens towards the outside. The
piston in its descending course presses the water ; this pressure shuts
the valve of the pump and opens that of the conducting pipe, and
forces the liquid out.

The Suction and Force-pump (Fig. 77) combines the arrangements
of both the pumps we have just described. The ascent of the water
is caused by suction ; and the piston, which is solid (i.e. is not fur-
nished with valves), in coming down presses the liquid into the
lateral tube.

106

PHYSICAL PHENOMENA.

[BOOK i.

We will now describe an instrument known to most people — the
siphon — which is of great use in transferring liquids from one vessel
to another : it is the pressure of the air which causes the action in
this case also. A tube formed of two curved branches, of unequal
length, is filled with part of the liquid which is to be transferred,
and its shortest branch is immersed in the vessel which contains
this liquid (Fig. 78). As soon as this is done, the liquid is seen to
flow from the openiug at the end of the longest branch as long
as the shortest remains immersed.

What is the cause of this continual flowing ? Nothing is more
easy to explain. At the surface of the liquid in the vessel, and at the

Fio. 78. — The siphon.

lower and free extremity of the tube, the atmospheric pressure is
exerted with almost equal intensity and in contrary directions. At
the point where the tube is in the vessel, this pressure serves to sustain
the liquid in the left-hand branch, and it would be maintained
there in equilibrium if the length of the two branches were the same
and both the ends were immersed in vessels at the same level. All
the portion of the liquid contained in the tube above the level of the

CHAP, ix.] WEIGHT OF THE AIR AND OF GASES. 107

vessel, remains in equilibrium under the influence of these opposite
pressures. There remains then in the large branch of the siphon a
column of water the gravity of which disturbs the equilibrium and
determines the direction of its flow.

Ifc might be imagined that when once the liquid in the tube
had escaped, the action would stop; but it must be remarked that
for this the two branches of the liquid would, need to be separated
by a vacuum, which the pressure exerted on the liquid in the vessel
by the atmosphere tends continually to fill, so that in reality this
separation never takes place, and the flowing continues.

The forms of siphons differ, according to the use to which they are
destined, and also according to the nature of the liquid to be transferred.
We describe some of them in the volume on the Applications of
Physics, when we explain their applications in great hydraulic works.

It remains for us to terminate the study of the phenomena of
gravity, by describing the instruments which are used to exhaust
the air from a receiver, or any vessel, or, on the other hand, to com-
press it there; and by stating how the pressures of gases are
determined, and according to what laws these pressures vary when
the volume which they occupy is made to vary.

Torricelli's experiment on the tube gave a very simple means of
making a vacuum, and a vacuum as perfect as possible ; for the
space situated above the column of mercury, which has received the
name of the barometric chamber, is almost a perfect vacuum. But if
the process is simple, it is far from being practical, since it would
necessitate the use of an enormous quantity of mercury, if the space
which we wished to rarefy were considerable, and moreover the pre-
cautions required to be taken at each operation would be irksome.
Thus long ago other means were sought. It was in 1654 that the
first air-pump was thought of and constructed. Otto de Guericke
was the inventor, and we have quoted many curious experiments due
to this able physicist. It soon received important improvements
from Boyle, Papin, Muschenbroek, and Gravesande. At first
it was only formed of one cylinder; but the necessity of having
two, to get rid of the great resistance which is felt while working
the one-cylinder instrument was soon obvious. We cannot give
the history in detail of the progress of any mechanical instrument,

108

PHYSICAL PHENOMENA.

[BOOK i.

and content ourselves with describing the air-pump as it is now used
by all physicists.

And first let us deal with the principal arrangements. Let us
imagine two cylinders, each furnished at the bottom with a valve
which opens upwards, and with a piston having an orifice closed by
a valve which opens in the same direction. The two orifices in the
base of the cylinder communicate by a common pipe with a well-
ground glass plate, on which the receiver is placed, and at the centre
of which is the opening of the pipe. Fig. 79 shows in section one
of the cylinders, its twa valves, and the communicating canal. The
action of this half of the instrument being well understood, it will
be easy to comprehend the whole.

Let us begin at the moment when the piston touches the lower part
of the cylinder. The receiver is filled with air at the atmospheric

pressure. At the moment
when we raise the piston, a
vacuum is made in the
lower part of the cylinder.
The air of the receiver
which filled the communi-
cating canal lifts up the
lower valve by its elastic
force and spreads itself in
the vacuum, the valve of
the piston being kept shut
by the pressure of the air
which is exerted externally

FIG. 79.— Action of the piston and valves in the air-pump. Qn ft-Q ^e gurface Qf ^he

piston. This passage of air from the receiver into the cylinder takes
place until the piston has reached its highest position. It is clear
that at this moment the quantity of air contained in the receiver has
diminished, and that it has diminished one-half, if the volume of
the cylinder is precisely equal to the volume of the receiver and canal.
Let us now send the piston in a contrary direction. At the moment
when it begins to descend, the capacity of the cylinder diminishes,
the pressure of the air which it contains increases, exceeds that of the
air of the receiver, and the lower valve is closed. Then, in propor-
tion as the descent of the piston lessens the capacity, the confined

CHAP. IX.]

WEIGHT OF THE AIR AND OF GASES.

109

air increases in density : on our assumption of its capacity, this
density will again become equal to that of the atmospheric air, as
soon as the piston attains half of its course. Beyond this point the
interior pressure increases, lifts up the valve of the piston, and the
air escapes altogether, until the piston again rests on the lower part
of the cylinder.

This single up-and-down movement, analysed in its effects, explains
the whole of the operation, as it has sufficed to rarefy the air in
the bell-jar one-half: that which remains will be again rarefied at a

Fio. 80.— Detail of the piston and
its valves.

Fits. 81.— Air-pump with two cylinders. Transverse
section.

second, then at a third trial, and so on. The pressure will become the
quarter, eighth, and then the sixteenth of the first pressure, as we
shall soon see in explaining Mariotte's law. This proportion would
of course change, if the ratio of the capacity of the cylinder to that
of the receiver were changed.

Figs. 80, 81, 82, and 83 will now explain the real arrangement of
the air-pump, and show the utility of the second cylinder. The first
shows how the two valves are placed, that in the piston and that at

PHYSICAL PHENOMENA.

[BOOK i.

the bottom of the cylinder. The valve of the piston is a small
plate, a, with a light spring pressure on the opening, but which gives
way to a very slight pressure in the contrary direction. The valve
of the cylinder, 6, is conical ; a rod, T, which moves by friction in
the piston, raises or lowers it, but only for a very short distance.
Fig. 81 shows that the rods of the pistons are formed with rackwork
which works into a pinion, so that, with the help of a handle with two
arms, it is possible to lower one piston and raise the other. Thanks
to this arrangement, the work done is doubled ; but — and this is
the end for which it was proposed — the resistance is reduced to its
minimum; for, in proportion as the vacuum is made, each piston

when rising must overcome the atmo-
spheric pressure which acts on its base ;
but, on the other hand, this pressure
helps the other piston to descend. In
this way, then, there is a compensation
or equilibrium between these two forces
which act indeed in the same direc-
tion, but all the force is done away with
by the resistance of the pump, without
fatiguing the operator. Figs. 82 and 83
give the plan and the exterior view of
the air-pump with two cylinders.

It will be seen how the pipe, which
unites the two cylinders by a tube, com-
municates at the centre with the plate,
which is of ground glass, perfectly plane,

on which is fixed the well-greased edge of the receiver in which
the vacuum is to be made. If the receivers have the form of tubes
or balls, &c., they are screwed into the aperture in the centre of
the plate.

A stopcock in the middle of the tube of communication is pierced
with holes, which enable us either to establish or close the communi-
cation between the pump and the receiver, or to permit the exterior
air to penetrate into the cylinders or into the receiver only.

In the same pipe, a bell glass (H, Fig. 83) is seen, containing a
barometric tube, or manometer, which is used to indicate to what
degree the exhaustion has proceeded in the receiver ; that is to say,

FIG. 82. — Plan of the air-pump with
two cylinders.

CHAP. IX.]

WEIGHT OF THE AIR AND OF GASES

111

what is the pressure of the quantity of air which this latter still
contains.

Lastly, the best air-pumps are furnished with an arrangement,
the invention of which is due to M. Babinet. This is a stopcock by
the aid of which, and a special pipe, the receiver is allowed to com-
municate with one cylinder only. The air which it still contains
is forced through another pipe under the piston of the second cylinder.

FIG. 88. — Exterior view of the air-pump.

and there, thanks to the increase of pressure which follows, it ends
by raising the valve. The degree of vacuum is thus extended to
a limit, such that the pressure of the air which still remains in
the receiver is scarcely appreciated by the manometer.

Bianchi's air-pump has only one cylinder. But the piston divides
into two compartments, which alternately receive and expel

the air: it is, properly speaking, a double-action pump.

Fig. 84

112

PHYSICAL PHENOMENA.

[BOOK T.

explains the manner in which this pump acts. A rod supports
the two movable conical valves, which shut and open alternately
under the action of the piston, thus opening and closing the com-
munication of each compartment with the receiver. The air of the
lower compartment, compressed when the piston descends, raises
a valve held by a spring, over the orifice of the pipe formed in the
piston-rod ; it escapes to the outside by this pipe. The air of the
upper compartment escapes by a valve of the same kind fitted to

the lid of the cylinder. A system of
toothed wheels is put into motion by a
handle ; and as the cylinder can oscillate
in a vertical plane, the alternate move-
ment of the piston is accomplished by
a continuous movement of rotation, the
velocity of which is regulated by a very
heavy fly-wheel (Fig. 85). With this
machine a vacuum can be rapidly pro-
duced in receivers, the capacity of which
may increase with the dimensions of the
cylinder.1

We have had already several times
occasion to describe some curious experi-
ments made by the aid of the air-purnp:
we shall in the sequel refer to others
connected with the phenomena of heat,

sound, and electricity. We shall content ourselves here by indicating
some which concern the phenomena of weight. For example, it is
proved that water ordinarily contains, in solution, air retained in it
by the atmospheric pressure. In the receiver, we see the bubbles
of air attached to the sides increase as the pressure diminishes,
and mount to the surface of the water. Smoke, which in the
atmosphere rises above the lower strata, falls in vacuo like a heavy

FIG. 84. — Bianchi's nir-]>uni]> ; interior
view of the cylinder.

1 M. Deleuil has constructed an air-pump specially intended for industrial uses,
the piston of which does not touch the walls of the cylinder. The thin stratum of
air which remains in the space serves as a fitting to the piston, so that the resist-
ance due to the friction of the piston in the ordinary cylinder is done away with.
M. Deleuil obtains in a receiver of 14 litres in capacity a degree of rarefaction
measured by 3 millimetres of pressure only.

CHAP, ix.] WEIGHT OF THE AIR AND OF GASES. 115

mass. This phenomenon shows that the principle of Archimedes
is true for gases as for liquids, as may be shown by another
experiment with a little instrument called a baroscope, the inventor
being Otto de Guericke. A balance supports at each end of its
beam two metallic balls, the one hollow and thin, the other solid
and of small volume : weighed in air, these two balls exactly
establish equilibrium (Fig. 86). When the apparatus is brought
beneath the receiver of the air-pump, we see the equilibrium dis-
turbed when the air is exhausted, and the beam is inclined towards
the largest sphere. This sphere lost then in the air a certain
portion of its weight, which is precisely equal to the weight of
the displaced air. This proves to us that to determine the exact

FIG. 86. -The baroscope. Fio. R7.— Condensing machine.

Interior view of the piston.

weight of bodies, it is necessary to weigh them in vacuo, or at least
to correct the error due to the pressure of the air. For delicate
weighing in chemistry, or for the precise determination of densities,
this correction is indispensable.

The application of the principle of Archimedes to balloons or
aerostats forms the subject of a future description.1

Instead of making a vacuum in a vessel or receiver, it is possible,
on the contrary, to accumulate and to compress the air or other
gases within it. This operation is accomplished by means of con-
densing machines or pumps.

1 Applications of Physics.

116

PHYSICAL PHENOMENA.

[BOOK r.

Condensing machines are constructed exactly like air-pumps,
with one modification — all the valves open in a contrary direction.
On examining Fig. 87, which represents a section of the con-
densing machine, it will be immediately seen what is the action

Fia. 88. — Silbermann's condensing pump*
Exterior view.

FIG. 89. — Silbermann's condensing
pump. Section.

of the mechanism, and how, instead of rarefying or expelling the
air, the oscillatory movement of the piston must on the contrary
accumulate and compress it.1

1 The condensing pump of this kind, of which we give the section and the
exterior view, is due to a physicist whose merit equals his modesty, M. J. Silber-
niann. The stopcock, the position of which is shown below the valves, enables
us to condense in the one. air or any other gas contained in the other ; to reverse

CHAP. IX.]

WEIGHT OF THE AIR AND OF GASES.

117

At the present day, condensing pumps formed with one cylinder,
with a solid piston, and with two valves placed at the bottom
of the cylinder, one communicating with the outer air, the other with

FIG. iK>. — Connected condensing pumps.

the receiver (Figs. 88 and 89), are used in preference. If a more rapid
compression is required, a pair of pumps are used. Fig. 90 shows
the general arrangement of instruments of this kind. M. Regnault

the order of communication of the receivers; or, again, to re-establish between
them equilibrium of pressure ; lastly, to make a communication between them and
the atmosphere. It is both an air-pump and a condensing pump.

118

PHYSICAL PHENOMENA.

[BOOK i.

used it to obtain air or vapour, the pressure of which was equivalent
to thirty times the atmospheric pressure, or capable of supporting a
column of mercury thirty times 76 centimetres ; that is, 22'80 metres.
Let us now state on what principle we rely to
estimate the pressures of gases, and what law the
variations of these pressures, under the influence of
the change of volume only, follow.

This law, the discovery of which is due to the
physicist Mariotte, is given thus : —

If a gaseous mass is submitted to a series of different
pressures, the volumes which it successively occupies
vary inversely as the pressures which it undergoes.
Here is an experimental demonstration of this law:
We take a long bent tube, the smaller arm of
which is closed, and the large one open (Fig. 91). If
it is perfectly cylindrical, the scale, divided into
equal parts, the divisions of which are seen on the
stand to which it is fixed, indicates in the tube equal
capacities. If it is not cylindrical, it is divided into
unequal portions of equal capacity.

Let us introduce a certain quantity of mercury,
and, by shaking, make the liquid extend in two
columns of the same height, the levels of which
correspond to the zeros of the two scales. At this
moment, equilibrium exists between the outer air
which presses the mercury in the large open arm.
and the interior air confined in the closed arm.
The pressure of the latter is then equal to that of
the atmosphere.

Let us pour mercury into the large arm.
Equilibrium will be disturbed, and the mercury will rise in the
closed arm. Let us stop when the level attains division 12;
that is to say, when the volume of gas has been reduced one-half.
We shall prove that the difference of the levels of the mercury
is precisely equal to the barometric height at the moment of
the experiment. Now, it is clear that at this moment it is this
difference of level which measures the increase of pressure of the
confined gas; the total pressure is then two atmospheres.

Fio, 91. — Experimental
prouf of Mariotte'a
law.

CHAP, ix.] WEIGHT OF THE AIR AND OF GASES. 119

On again pouring mercury into the large arm, we shall see the
level rise in the smaller branch as far as the divisions 16, 18, 19.2
for example, which supposes the volume of gas reduced to a third,
quarter, and fifth of its original volume. Now, it is found that the
pressures are successively three, four, five atmospheres. Generally,
the volume occupied by the air or by any other gas varies precisely
in inverse ratio to the pressures which this gas supports ; which
proves the law. The law is proved with the same facility when
we submit the gaseous mass to decreasing pressures : lower than the
atmosphere the volume increases as the pressures diminish.

It is seen by this law, the importance of which is extreme, how
gases are compressible, and how they differ in this respect from liquids
the compressibility of which is confined within very narrow limits.

In the preceding experiments, the temperature is supposed
constant.

If Mariotte's law were exactly true, it would follow that all gases
are endowed with equal compressibility, and that it increases how-
ever great the pressures to which they are submitted. Dulong and
Arago have proved the exactitude of the law, for air, to 27 atmo-
spheres ; but M. Despretz and M. Eegnault (later) have arrived
at the conclusion that this compressibility is not precisely the same
for all gases, and, moreover, that it is slightly variable for the same
gas. Air, nitrogen, and carbonic acid are really condensed more than
Mariotte's law would allow ; hydrogen acts in a contrary direction.
As to the gases susceptible of passing into a liquid state, the variation
has been found much more considerable, according as the experiments
have been made at a temperature nearer that at which they are
liquefied. Doubtless, at this temperature the gases undergo mole-
cular modifications the nature of which is not yet known, but which
differ from the effects due to the variations of pressure. The
measure of the pressure of the air which remains under the receiver
of the air-pump when a vacuum is made, a measure effected with
the help of a manometer or short barometer, is a direct application
of Mariotte's law.

BOOK II.

SOUND.

BOOK II.
SOUND.

CHAPTEE I.

THE PHENOMENA OF SOUND.

THE absence of all sound, of all noise, in a word absolute silence,
is to us synonymous with, immobility and death. We are so
accustomed to hear, if it is only the noise we ourselves make, that
we can scarcely conceive the idea of a world completely silent and
dumb, as the moon appears to be, if we are to believe astronomers.

Phenomena of sound are perpetually manifested on the earth,
although of course there is in this respect a vast difference between
our great cities, the thousand noises of which are perpetually
deafening us, and the low and confused murmur which is heard in the
solitude of the fields, on the mountains, or in the plains. We cannot
fail to be struck by the contrast between the calm of the Alpine and the
Polar regions, in which all life disappears, and the resounding shores
of the ocean ! There the silence is broken only by the dull rolling
of avalanches, the cracking of ice, or the roaring of violent gusts
of wind. The rumbling of thunder, so prolonged in the plains or
in valleys, does not exist on the highest mountains : instead of the
terrible report which generally characterizes thunderclaps, the reper-
cussion of which multiplies their duration, we have there a harsh
sound, similar to the discharge of fire-arms. On the sea- shore, on the
contrary, the ear is deafened by the continuous sound of the waves
which break in foam on the rocks, and by the dull, uniform roaring

L 2

124 PHYSICAL PHENOMENA. [BOOK ir.

which like a solemn bass accompanies the sharper notes which the
waves produce when they strike the sand and pebbles. In the
midst of fields arid forests the sensation is quite different. We hear
a low moaning formed by the union of a thousand varied sounds:
the grass which bends under the wind, the insects which fly or creep
about, the birds whose voices are lost in the air, the sound of the
branches of the trees which rustle under the impulse of the light
breeze, or which are bent and broken by violent winds. From all
this comes a harmony, sometimes gay and sometimes grave, but
always different from the discordant clatter which fills the populous
streets of great towns.

Watercourses, rivers, brooks, and torrents join their notes to this
concert ; in mountainous countries there is the noise of cascades
which dash upon the rocks, and sometimes the terrible roaring of
falling rocks which destroy and bury everything in their passage.

But of all natural sounds, the most continuous and violent are
those which arise and are propagated through the atmosphere:
masses of air dragged along by an irresistible movement, sometimes
shrieking, sometimes roaring with fury, strike against all obstacles
which oppose them, such as the unevenness of the ground, mountains,
rocks, forests, or -solitary trees. When electricity is associated with
these actions they become more terrible, and the frightful reports of
thunder drown all other sounds. Volcanic explosions and earthquakes
alone rival in power this great voice of nature. An immense
detonation was heard under the towns of Quito and Ibarra, arising
from the catastrophe which destroyed Eiobamba in February 1797 ;
but, curiously, it was not heard at the place of the disaster. The
upheaval of Jorullo, in 1759, according to Humboldt, was preceded
by subterranean roarings which lasted two entire months.

To complete this list of sounds naturally produced in the earth
and the atmosphere, there remains for us to mention the detonations
which accompany the fall of cosmical meteors, aerolites, and bolides.
These explosions usually occur at great heights, and persons who have
heard them compare them either to the discharge of artillery or to
the prolonged rolling of thunder.

The phenomena of sound which are most interesting to us are
those which men and animals produce by the aid of special organs :
the human voice, that indispensable interpreter of our thoughts and

CHAP, i.] THE PHENOMENA OF SOUND. 125

sentiments ; and the cries of animals, which express in a ruder mariner
their various impressions, their wants, joys, and their griefs. The
most powerful of all arts — music — was created by man to express
that which articulated language could not express ; and to add still
more to the gifts of nature, he has discovered how to multiply the
resources of his voice by the aid of various instruments.

The necessities of labour and of human industry have caused man
to produce many other sounds and noises which do not commend
themselves either for melody or harmony, but most of which are
inseparable from the works in which they originate, and share,
so to speak, in their character of utility. In manufactories, work-
shops, and forges, the noise of hammers and saws, of all sorts of
tools, and of steam-engines, often continues uninterruptedly night and
day. But how can it be helped ? To our thinking, it is a music which
is infinitely preferable to that of musketry and cannon on the field of
battle ; just as far as the contest of work and of science is higher than
the action of brute force.

However varied the several phenomena we have passed in review
may appear, they all relate in reality to one mode of movement, of
which we must study the nature and formulate the laws. We will
commence by enumerating the different ways in which sound can be
produced and propagated, in solids, liquids, and gases.

126 PHYSICAL PHENOMENA. [BOOK n.

CHAPTEE II.

PKODUCT10N AND PKOPAGATION OE SOUND. — REFLECTION OF SOUND. —
VELOCITY OF SOUND IN DIFFERENT MEDIA.

Production of sound by a blow or percussion, and by friction, in solids, liquids, and
gases — Production of sound by the contact of two bodies at different tem-
peratures ; Trevelyan's instrument — Chemical harmonicon — The air a vehicle
of sound ; transmission of sound by other gases, by solids and liquids — Pro-
pagation of sound at great distances through the intervention of the ground —
Velocity of sound through air ; influence of temperature ; experiments of
Villejuif and Montlhery — Velocity of sound in water ; experiments made
on the Lake of Geneva, by Colladon and Sturm — Velocity of sound through
different solid, liquid, and gaseous bodies.

PEKCUSSION, or the shock of two bodies against each other, is
one of the most usual methods by which sound is produced.
The hammer which strikes the anvil, the clapper which causes bells
to sound, drumsticks, the rattle, and a hundred other instances which
the reader will easily call to mind, are examples of the production of
sound by the percussion of solid bodies. The most varied noises
can thus be obtained, but we shall find that this variety depends both
on the form and the nature of the sonorous body and on the way in
which the sound is conveyed to our ears. In the water-hammer
experiment, the noise proceeds from the shock of a liquid mass
against a solid body.

Friction is another cause of the production of sound or noise:
thus it is that by the aid of a bow, the horsehairs of which have
been rubbed with a resinous substance called colophane, the expended
cords of certain stringed instruments are made to resound; so also
in the case of bells of glass or metal. Sounds are also obtained by
longitudinal friction applied to cords or metallic rods. When certain
substances, such as wood, stone, &c., are drawn along the ground, they

CHAP, ii.] PRODUCTION AND PROPAGATION OF SOUND. 127

produce a noise which is due to friction : carriage-wheels which roll
along the roadway also produce a sound which is due in great part to
friction, but also to some extent to percussion. The act of drawing
aside a tense cord, as is usual in playing instruments like the guitar,
harp, or mandoline, produces a sound which is due both to percussion
and to friction.

When liquid and solid bodies are brought into contact by means
of percussion or friction, sounds and noises are produced; but the
same movements in liquids, without the intervention of solid bodies,
also produce sound : such is the agitation which is produced by the
Ml of raindrops on the surface of a pond or river.

In gases, sound, as we shall presently see, is caused by a series
of condensations alternating with dilatations ; but it may also be
induced by percussion or friction. Thus, the air hisses when it re-
ceives a violent stroke from a cane or whip : arid the wind produces
loud sounds when it strikes against trees, or houses, or other solid
bodies. The roaring sound which is sometimes heard in chimneys
is due to a movement of the air which we shall study when
we consider the nature of the sounds produced by the movement
of gases in tubes. Of the same kind is the sound produced by those
musical instruments which are known as wind instruments. The
human voice and the cries of animals belong also to this class.

Explosions of gases, the noise which accompanies the electric
spark and the reports of gunpowder, are sounds caused by rapid
changes of volume, and by successive dilatations and contractions of
gaseous masses. Among the most remarkable modes of producing
sound, we may mention the contact of two solid bodies at different
temperatures. This singular phenomenon was described for the first
time in 1805, by Schwartz, the inspector of a Saxon foundiy. Having
placed a silver ingot at a high temperature on a cold anvil, he was
astonished to hear musical sounds during the cooling of the mass.
In 1829, Arthur Trevelyan accidentally placed a warm soldering
iron on a block of lead ; almost immediately a sharp sound was heard.
He was thus induced to study the phenomenon under different con-
ditions, and he invented various instruments to illustrate the cause
of the production of this sound. These will be described when we
speak of sonorous vibrations.

The passage of an electric current produces sound in a bar of

128

PHYSICAL PHENOMENA.

[BOCK ir.

iron suspended at its centre, arid one extremity of which is in the
centre of an induction coil.

Lastly, the combustion of gases in tubes gives rise to the production
of musical sounds. If we light a jet of hydrogen generated by the
small apparatus called by chemists the philosophical lamp, and intro-
duce it into the interior of a tube of greater diameter than itself and
open at both ends, we hear a sharp or dull sound, which varies with
the length, diameter, thickness, and nature of the substance of the

tube. If several of these tubes
are arranged together, a series
of musical sounds may be ob-
tained, and tunes may be pro-
duced. Hence the name of
" chemical harmonicon " by
which this musical instrument
is known. This fact was the
starting-point of the curious
experiments of Schaffgotsch
and Tyndall on singing flames.
Hitherto we have considered
the production of sound or
noise in sonorous bodies which
may be either solid, liquid, or
gaseous ; let us now inquire
how sound, that of a clock
which is striking, for instance,
reaches our ears. We can
answer this question by means
of observations and very simple
understand the real nature of the

FIG. 92. — Philosophical lamp or chemical harmonicon.

experiments, even before we
phenomenon of sound.

It is a well-known fact that sound takes an appreciable time to
travel from a sonorous body to the ear. When we see a person at
some distance from us who is striking blows with a hammer, we see
the hammer fall before we hear the noise of the percussion. In the
same way the report of a gun or cannon reaches the ear after the
flash produced by the explosion has been visible to the eye. In all
these cases, the interval included between seeing the flash and hearing

CHAP, ii.] PRODUCTION AND PROPAGATION OF SOUND.

129

the sound, indicates a difference between tho velocity of light and
that of sound ; but as the velocity of light, compared with that of
sound, may be considered as infinite, this interval gives without any
perceptible error the time which sound takes to be propagated from
one point to another. We learn by daily observation that this
interval increases with the distance. I remember having admired on
the coast of the Mediterranean the curious spectacle of a man-of-war
practising with cannon. I saw the smoke of the guns, then the
ricochet of the cannon-balls on the crests of the waves, long before
I heard the thunder of the report.

Sound is propagated by a succession of impulses : we shall soon
learn with what velocity. But what is
the medium which serves as a vehicle to
this movement ? Is it the ground ? Is
it communicated by the intervention of
solids, liquids, or the air, or by these
several media at once ? The following
experiment will answer these questions.

Let us place under the receiver of an
air-pump a clockwork arrangement fur-
nished with a bell, the hammer of which
is temporarily fixed, but is capable of being
moved at will by a rod (Fig. 93). Before
exhausting the receiver, the bell is dis-
tinctly heard when struck by the hammer.
But in proportion as the air is rarefied
the sound diminishes in intensity; and
as soon as the vacuum is approximately
perfect, it is completely lost if the precau-
tion has been taken to place the appa-
ratus on a cushion of cork, or wadding, or any substance which is soft
and more or less elastic. The hammer is then seen to strike the
bell, but no sound can be heard. If we now introduce into the
receiver any other gas, such as hydrogen, carbonic acid, oxygen,
ether-vapour, &c., the sound is again heard. Thus air and all gases are
vehicles of sound. But they do not all possess this property to the
same extent. Thus, according to Tyridall's experiments, the conduc-
tivity of hydrogen gas for sound is much less than that of air, at an

FIG. 93. — Sound is not piopagated in
a vacuum.

130 PHYSICAL PHENOMENA. [BOOK IT.

equal pressure, while the velocity of propagation is nearly four times
greater in hydrogen than in air.

Solid bodies also transmit sound, but in very varied degrees
depending on their elasticity. Thus in the preceding experiments,
even when the vacuum is nearly perfect, if we place the ear close
to the receiver, we hear a very feeble sound transmitted to the sur-
rounding air by the cushion and the plate of the air-pump. The
transmission of sound through solids is proved even better by the
fact that the sound of the bell is simply enfeebled if we place the
clockwork apparatus on the glass plate of the air-pump without the
intervention of a soft cushion.

Water, and liquids in general, are also vehicles of sound, and as
regards intensity and velocity they are better conductors than air. A
diver when under water hears the least noise ; for example, that made
by flints rolling and knocking against each other.

We must not confound the sounds which we perceive through the
medium of the air with those which solids such as the ground or
elastic bodies transmit to us. If the ear be placed at the extremity
of a rather long piece of wood, we can clearly distinguish the noise
produced by the friction of a pin or the tip of a feather at the oppo-
site extremity, while a person standing near the middle, but with his
ear not close to the wood, hears nothing. The ticking of a watch
hung at the end of a long tube of metal is distinctly heard at the
other end, while those near the watch do not perceive any sound.
Hassenfratz, "having descended one of the quarries under Paris,
instructed some one to strike the walls of one of the subterranean
galleries with a hammer : he gradually went further away from the
point where the blows were given, and on placing his ear against the
wall he distinguished two sounds, one being transmitted by the stone
and the other by the air. The first arrived at the ear much sooner
than the other, but it also died away much more rapidly in pro-
portion as the observer removed further from the source, so that it
ceased to be heard at the distance of a hundred and thirty -four paces,
while the sound transmitted by the air only ceased to be heard at a
distance of four hundred paces." (Haiiy.)

Similar experiments, when tried with long wooden or iron bars,
give the same result, both as to the higher velocity and reduced
intensity.

CHAP, ii.] PRODUCTION AND PROPAGATION OF SOUND. 131

Humboldt, in describing the dull noises which nearly always
accompany earthquakes, quotes a fact which shows the facility with
which solid bodies transmit sound to great distances. " At Caracas,"
he says, " in the plains of Calabozo and on the borders of Eio-Apure,
one of the affluents of the Orinoco, that is to say over an extent of
130,000 square kilometres, one hears a frightful report, without
experiencing any shock, at the moment when a torrent of lava flows
from the volcano Saint- Vincent, situated in the Antilles at a distance
of 1,200 kilometres. This is, as regards distance, as if an eruption of
Vesuvius was heard in the North of France. At the time of the
great eruption of Cotopaxi in 1744, the subterranean reports were
heard at Honda, on the borders of Magdalena : yet the distance
between these two points is 810 kilometres, their difference of level
is 5,500 metres, and they are separated by the colossal mountainous
masses of Quito, Pasto, and Popayan, and by numberless ravines
and valleys. The sound was evidently not transmitted by the air,
but by the earth, and at a great depth. At the time of the
earthquake of New Granada, in February 1835, the same phe-
nomena were reproduced in Popayan, at Bogota, at Santa Maria,
and in the Caracas, where the noise continued for seven hours
without shocks ; also at Haiti, in Jamaica, and on the borders of
Nicaragua."

To resume : the transmission of sound from a sonorous body to
the ear can be effected through the medium of solids, liquids, or gases,
but the atmosphere is the most usual medium. Hence it follows that
there is no sound beyond the limits of the atmosphere. The noise
of volcanic explosions, for example, cannot reach the moon ; and in
like manner the inhabitants of the earth do not hear sounds which
may be produced in interstellar spaces. The detonations of aerolites
therefore prove that these bodies at the moment of explosion are
within our atmosphere, the limits of which have not been pre-
cisely determined. On high mountains the rarefaction of the air
produces a great diminution in the intensity of sounds. Accord-
ing to Saussure and others, a pistol fired at the top of Mont
Blanc makes less noise than a small cracker. Ch. Martins, in
describing a storm which he witnessed in these high regions, says,
"The thunder did not roll; it sounded like the report of fire-
arms." Gay-Lussac, during his celebrated balloon ascent, remarked

132

PHYSICAL PHENOMENA.

[BOOK ii.

that the sound of hid voice was considerably weakened at a height
of 20,000 feet.

Let us now inquire with what velocity sound is propagated
through the different media we are about to describe ; and first of
the velocity of sound through air.

Many scientific men of the last centuries, among whom were
Newton, Boyle, Mersenne, and Flamsteed, endeavoured to determine

FIG. 94.— Measure of the velocity of sound through air, between Villejuif and Montlht-ry, in 1SL'±

this velocity, either theoretically or by experiment, but the numbers
at which they arrived were either too low or too high. We owe the
first precise experiments to the commission of the Academic des
Sciences in 1738. Again, in 1822, several physicists made deter-
minations in the same manner, and the following was their method
of proceeding. They were divided into two groups, which were
placed respectively at Montlhery and at Villejuif, these two stations
being chosen because there was no obstacle to interfere with sight.

CHAP, ii.] PRODUCTION AND PROPAGATION OF SOUND. 133

Gay-Lussac, Humboldt, and Bouvard were at Montlhery ; Prony,
Arago, and Mathieu at Villejuif. They were each provided with a
good chronometer; and two pieces of cannon of equal bore, charged
with cartridges of the same weight, were placed at each of the
stations.

The experiments began at eleven o'clock in the evening, with a
serene sky and a nearly calm atmosphere. Twelve alternate shots at
intervals of ten minutes were fired from each station, starting from a
given signal, and each group of observers noted the number of
seconds which elapsed between the appearance of the light and the
arrival of the sound. The mean of the diffeient numbers was 54
seconds 6 tenths ; and as the distance of the two pieces of artillery,
carefully measured, was 18,612 metres 5 decimetres, they concluded
that sound travels 340 metres 9 decimetres a second (1118'152 feet)
in nir at a temperature of 16° C. The reciprocity of the determi-
nations was in order to compensate for the influence of the wind.
The temperature of the air exercises an influence which theory
and experiment have equally confirmed. If the temperature in-
creases, sound is propagated with much greater rapidity ; and the
velocity diminishes with the fall of temperature.1

But because the velocity of sound varies with the temperature, and
also as we shall presently see with the humidity or hygroinetric state
of the air, the results obtained are probably more or less inexact.
The strata of air in which sound is propagated are far from being
homogeneous, and it is now known that their temperature during the
night increases with the height. To avoid these different causes of
error, M. le Roiix measured in a direct manner the velocity of
sound through a mass of air contained in a cylindrical tube of
72 metres in length. The air was dried, and its temperature kept
at 0° by surrounding the tube with ice. The sonorous impulse
was produced by the single blow of a wooden hammer, which was
caused to strike a membrane of caoutchouc stretched over one of
the extremities of the tube. This impulse, after having travelled

1 In addition to the preceding experiments, we must quote those of Benzenberg
in 1811 ; Goldingham in 1821 ; Moll and Van Beeck, Stampfer and Myrbach
in 1822 ; lastly, of Bravais and Martins in 1844. If we reduce the various deter-
mined velocities to zero,, and calculate tliem as having been made in dry air, we
obtain as a result a mean of 332 metres, or 1088'96 feet a second.

134 PHYSICAL PHENOMENA. [BOOK n.

along the tube, set in motion a second membrane stretched at the
other extremity of the tube. Lastly, the beginning and the end
of the propagation were registered automatically by electricity,
and its duration measured by a particular kind of chronoscope.
Numerous experiments gave M. le Eoux a velocity of 330*66 m.
a second : a number almost identical with the velocity, at the
same temperature, 0°, indicated by the experiments of the Bureau
des Longitudes in 1822.

If we adopt this last number, we deduce for the velocity
of sound at different temperatures, from — 15° C. to 50° C., the
following numbers : —

VELOCITY OF SOUND IN AIR.

Number of metres Number of yards

Temperature (C.) per second. per second.

— 15° 321-46 350-92

- 10° 326-23 356-10

— 5° 327-62 357-60

0° ...... 330-66 360-90

+ 5° 3,33-67 ...... 364-18

-f 10° . ... . . . 333-66 364-17

+ 15° 339-62 370-73

+ 20° 342-55 373-89

+ 25° 345-46 377'05

+ 30° 348-34 380-22

-f 35° .- 351-20 383-39

+ 40° 354-04 386-40

-f 45° ...... 356-85 389-50

4-50° 359-65 392-56

The experiments of 1738 and 1822 not only resulted in the deter-
mination of the velocity of sound ; they also proved that this velocity
is not modified by variations of atmospheric pressure : that the wind
increases or diminishes it according as it blows in the same or in a
contrary direction, whilst it does not effect any change if it blows in a
direction perpendicular to that of the transmission of the sound.

Furthermore, this velocity is uniform at every portion of the
distance traversed, and it is the same with sharp or dull sounds,
feeble sounds, or those whose intensity is considerable. We are
all aware that neither the time nor the precision of a piece of
music executed by an orchestra is altered, whatever may be its
distance from the listener. When the distance increases, all the
sounds are lessened in the same degree, but this is the only alteration

CHAP, n.] PRODUCTION AND PROPAGATION OF SOUND.

135

which they suffer, which could not happen if tones or sounds of
different intensity were propagated with different velocities. Lastly,
the velocity of sound through air appears to be the same in a
horizontal, vertical, or oblique direction. This fact results from the
observations made in 1S44 by Martins and Bravais, between the
summit and the base of the Faulhorn, and by Sta'mpfer and Myrbach
at two stations situated at different heights above the level of the sea,

FIG. 95. — Experimental determination of the velocity of sound through water

Very singular consequences follow from the difference which exists
between the velocities of light, sound, and projectiles. Thus the
soldier struck by a cannon-ball can see the fire which comes from the
mouth of the cannon, but he does not hear the noise because the
velocity of sound is less than that of the bullet ; but if he is struck
at a great distance, as the resistance of the air diminishes more and
more the velocity of the projectile, it may happen that he both sees
the light and hears the shot before he is struck.

136

PHYSICAL PHENOMENA.

[BOOK IT.

Sound is propagated through water with about four-and-a- quarter
times its velocity through air. This was shown by some experiments
made on the Lake of Geneva by two scientific men, Golladon and
Sturm. Their mode of experimentation was as follows. The observers
were seated in boats, one moored at Thonon, the other on the opposite
shore of the lake. The sound was produced by the stroke of a hammer
on a bell immersed in the water, and at the other station, a speaking-

FIG. 96. — Experiments made on the Lake of Geneva, V>y Collation ami Sturm.

trumpet, having a mouth of large aperture, also under the water,
received the sound propagated by the liquid mass by means of a sheet
of metal placed over the opening. The observer, whose ear was placed
at the mouth of the trumpet, was furnished with a chronometer or
chronograph, which indicated seconds and fractions of a second; and
he was made aware of the precise instant when the bell was struck by
the flash produced by the ignition of some powder, which was ignited
by the lowering of a lighted match fastened to the hammer in the

CHAP, ii."1 PRODUCTION AND PROPAGATION OF SOUND.

137

form of a lever. Figs. 95 and 96 indicate the arrangement, which will
be easily understood without a more detailed explanation.

The distance of the stations — 13,487 metres — was traversed by
the sound in nine seconds and a quarter, which gives 1,435 metres for
the velocity of sound in water at a temperature of 8° 0.

Lastly, the velocity of sound in solid bodies has also been ex-
perimentally determined. M. Biot, having operated on a cast-iron
pipe 951 metres in length, found that sound is propagated through
this metal with a mean velocity of 3,250 metres a second, which
is more than, nine-and-a-half times the velocity through air at the
same temperature.

The velocities of sound per second in different media, solid,
liquid, and gaseous, are as follows : —

Velocity of sound through gases at 0° .

Velocity of sound through liquids

Velocity of sound through solids

l Air 362 yards or 331r

J Oxygen 317

Hydrogen 1270

Carbonic acid 262

Water of the Seine at 15° . . 1437r

Sea-water at 20° 1453

„ at 23° 1160

Ether at 0° 1159

Tin 2498'1

Silver 2684

Platinum 2701

Oak, walnut 3440

Copper 3716

Steel, iron 5030

Glass 5438

Fir-wood 5994

138 PHYSICAL PHENOMENA. [BOOK n.

CHAPTER III.

PROPAGATION OF SOUND. — PHENOMENA OF THE REFLECTION AND
EEFEACTION OF SOUND.

Echoes and resonances — Simple and multiple echoes ; explanation of these
phenomena — Laws of the reflection of sound ; experimental verification —
Phenomena of reflection at the surface of elliptical vaults — Experiments
which prove the refraction of sonorous impulses.

WE shall learn hereafter that light and heat are propagated directly
by radiation and indirectly by reflection. Moreover, when this
propagation takes place through media whose nature and density
differ, the direction of the luminous and calorific waves undergoes
a particular deviation known to physicists as refraction.

The same phenomena of reflection and refraction occur in the
case of sound as in that of heat and light, and they follow nearly the
same laws.

That sound is reflected, when in being propagated by the air or
any other medium it strikes against an obstacle, is a fact with which
every one can make himself familiar by observation.

Echoes and resonances are phenomena due to the reflection of
sound. When we stand in a large room, the walls of which are not
covered with objects, such as curtains, which stifle sound, we notice
that our voices are strengthened, and the sound of steps or of
sonorous bodies is heard with great distinctness. In a still larger
room words appear doubled, which often renders them difficult to
be understood. This strengthening of sound, due to reflection from
walls, &c., is what is called resonance.

If the distance from the observer to the reflecting surface ex-
ceeds 65J feet (20 metres), he distinctly hears each word which he

CHAP. III.]

PROPAGATION OF SOUND.

139

pronounces a second time : this is the simple echo. If each word is
repeated two or three times, it is a multiple echo.

Let us understand the cause of these various phenomena.

However short the duration of a sound may be, the sensation
which it induces in the ear of the listener remains a certain per-
ceptible time, which is about -^ of a second. During this time
sound travels nearly 34 metres, so that if the distance A o from the
observer to the reflecting surface (Fig. 97) is less than 17 metres, the
sound of the word which he has pronounced has time to reach the
wall and return to his ear before the sensation is entirely exhausted.
The reflected sound will then be blended with that which he hears in
a direct manner ; and as
a number of partial reflec-
tions are produced in dif-
ferent parts of the room, a
confused murmuring will
follow, which is called a
resonance. The same ex-
planation applies to the
case of two or more per-
sons occupying the same
room and speaking either
separately or together, and
the resulting confusion of
sound would become
greater as the rapidity of
utterance increased.

If now the distance o A exceeds 17 metres, when the sound of the
syllable is reflected to the ear the sensation is ended, and we hear a
repetition more or less feeble of the direct sound. This is an echo.
The greater the distance, the greater will be the number of syllables
or distinct sounds. For example, let us suppose this distance to be
180 metres, and that in one second the observer pronounces three
syllables, the words being Answer me. To go to the reflecting surface
and to return, the sound takes a little over a second ; the direct
sensation is ended, and the ear hears for the second time, distinctly,
Answer me. This is a simple echo.

A multiple echo occurs between distant parallel reflecting surfaces.

M 2

Fio. 97. — Reflection of sound. Phenomena of resonance.

140 PHYSICAL PHENOMENA. [BOOK IT.

In this instance the sound reflected by one of them is reflected a
second time from another, and so on; but obviously, by these
successive reflections, the sounds are weakened more and more.
Edifices, rocks, masses of trees, even clouds, produce the phenomenon
of echo. Among the most curious is the echo of the chateau of
Simonetta, in Italy, which repeats the words spoken as many as forty
times between the parallel wings of the edifice. We find in the
Cours de Physique, of M. Boutet de Monvel a curious fact, which
visitors to the Pantheon can verify. In one of the vaults of this
building, "it is sufficient for the guide who shows them to strike a
sharp blow on the front of his coat to awaken in these resounding
vaults a noise nearly equal to that of a cannon." This is a phe-
nomenon of echo, and of concentration of sound.

In ancient and modern works a number of instances of multiple
echoes are mentioned, the more or less surprising effects of which
may be questioned, but they are all easily explained by the suc-
cessive reflections of sound.

Such an one existed, it is said, at the tomb of Metella, the wife
of Crassus, which repeated a whole verse of the ^Jneid as many as
eight times. Addison speaks of an echo which repeated the noise of
a pistol-shot fifty-six times. It was noticed, like that of Simonetta,
in Italy. The echo of Verdun, formed by two large towers about
52 metres apart, repeats the same word twelve or thirteen times.
The great pyramid of Egypt contains subterranean chambers con-
nected by long passages, in which words are repeated ten times.
Again, Barthius speaks of an echo situated near Coblentz, on the
borders of the Rhine, which repeats the same syllable seventeen
times. This had a very peculiar effect, because the person who
spoke was scarcely heard, whilst the repetitions produced by the
echo were very distinct sounds. Among echoes in England we
may note one in Woodstock Park, which repeats seventeen syllables
by day and twenty by night; while in the Whispering Gallery of
St. Paul's the slightest sound is answered from one side of the
dome to the other.

While living, for some years, on the sea-coast of Hyeres, I heard a
most magnificent echo : for a whole morning, reports of artillery fired
from a vessel anchored in the roads were reflected from the sides of
the mountains on the coast in prolonged echoes, which made me at

CHAP, in.] PROPAGATION OF "SOUND. 141

first imagine the presence of a whole lleet ; the effect was like that
of thunderclaps. A single discharge seemed to last a minute.

The reflection of sound is subject to very simple laws, of which
we shall now give an outline. As we shall presently see, they result
from the nature of the vibratory movement which constitutes sound,
and they are also experimentally proved.

To explain this, let us imagine for the present a sound-ray, like
a ray of light, to start from a centre of disturbance and follow a
right line. When this ray comes in contact with a reflecting surface,
let us call it an incident ray; then the reflected ray is the line
along which the sound rebounds from this surface into the medium
whence it came. The angles which the incident and reflected rays
form with a line perpendicular to the surface at the point of inci-
dence are called respectively the angles of incidence and reflection.
These definitions being clearly understood, the following are the laws
of the reflection of sound : —

First law. — The incident sound-ray and the reflected sound-ray are
in the same plane with the line perpendicular to the surface at the
point of incidence.

Second law. — The angle of incidence is equal to the angle of reflection.

The experimental proof of these laws is very simple. Let us place
two metallic mirrors of a para-
bolic form — that is, obtained by
the revolution of the curve called
a parabola about its axis (Fig. 98)
— face to face in such a manner
that their axes coincide. The
parabolic curve is necessary be-
cause it possesses, near its sum- X7 "
mit A, a focus F, to which all \v
lines such as MZ, parallel to the N^

axis AF, impinging Upon differ- Fto. 98. -Property of the parabola,

ent points of the parabola, are

reflected. The rays proceeding from the focus and those parallel
to the axis, form equal angles with the normals to the parabola, at
every point, such as the point M. All rays parallel to the axis coming
in contact with the parabola will be reflected to the focus at F.

142

PHYSICAL PHENOMENA.

[BOOK n.

Now, if a watch is placed in the focus of one of these parabolic
mirrors, the sound-rays or sonorous waves produced by the ticking
movement will be received on the mirror and reflected parallel to the
axis ; they then will strike the concave surface of the second mirror
and be concentrated at its focus. The observer, who must employ a
tube in order not to intercept the waves, will easily hear the sound
of 'the watch if he places the extremity of the tube at the focus
of the second mirror (Fig. 99). The sound is heard nowhere else,
even by persons who place themselves near the space between the
two mirrors, and at a short distance from the watch.

Fia. 99 —Experimental study of the laws of the reflection of sound.

The curve called an ellipse has two foci, and the rays sent from
one are reflected to the other. A room with an elliptic roof should
therefore produce the same phenomenon as the two parabolic mirrors ;
and this is confirmed by experiment. The Museum of Antiquities
at the Louvre possesses a room of this kind, in which two persons
placed at the opposite extremities of the room in the two foci, are
able to converse in a whisper, utterly regardless of the presence of
persons who are in other positions.

CHAP. III.]

PROPAGATION OF SOUND.

143

Eefiection of sound is made use of in many instruments, which
we shall have occasion to describe when speaking of the applications
of physics to the sciences and arts.

Sound is propagated, as we have before seen, by all elastic media,
but with varying velocities, which depend in a certain degree on
the density of the medium. When sound passes from one medium
to another, its velocity changes ; and if it enters the second medium
obliquely, a deviation of the sonorous wave results, which deviation
brings the ray nearer the normal to the surface of separation of the

FIG. 100. — Reflection of sound from the surface of an elliptical roof.

two media, if the velocity is less in the second than in the first.
When a ray enters a prism in which it is retarded, light undergoes
a similar deviation, which was proved by experiment long before the
true theoretical explanation was discovered ; and as the phenomenon
has been long known as refraction, the name of refraction of sound
has been given to the similar deviation of the sound-waves. M.
Sondhauss has placed the existence of this deviation beyond doubt
by the following experiment. He made a lens of collodion, and
filled it with carbonic acid gas. In this gas, the velocity of sound is

144

PHYSICAL PHENOMENA.

[BOOK ii.

less than in air. The sonorous waves which impinged upon the
convex surface of the lens were refracted on passing through the
gas, and, issuing on the opposite side, were brought to a focus. If
a watch is placed in the axis of the lens on one side, there is on the

FIG. J01. — Sonorous refraction. M. Sondhauss's instrument.

axis at the other side a point where the ticking of the watch is
heard distinctly, and better than in any other place. There is there-
fore an evident convergence of the sonorous waves towards the
conjugate focus of the lens ; and in this we have a proof of the
refraction of sound. The following are the laws which it obeys : —

First law. — The incident sound-ray and the refracted sound-ray
are in the same plane with the line perpendicular to the surface at
the point of incidence.

Second law. — If any points "be taken, one on the incident and
one on the refracted ray, at equal distances from the point of
incidence, and perpendiculars le drawn from them on the line
perpendicular to the surface at the point of incidence, the ratio
between these perpendiculars is constant.

CHAP, iv.] SONOROUS VIBRATIONS. 145

CHAPTEE IV.

SONOROUS VIBRATIONS.

Experiments which prove that sound is produced by the vibratory movement of
the particles of solid, liquid, and gaseous bodies— Vibrations of a cord, rod, or
bell — Trevelyan's instrument — Vibrations of water and of a column of air-
Nature of sound : pitch, intensity, and clang-tint — The pitch depends on the
number of vibrations of the sounding body ; Savart's toothed wheel ; Cagniard-
Latour's and Seebeck's syrens— Graphic method — Variable intensity of sound
during the day and night — Limit of perceptible sounds.

SOUND is a vibratory movement.
Sonorous bodies are elastic bodies, the molecules of which, under
the action of percussion, friction, or other modes of disturbance,
execute a series of alternating movements across their position of rest.
These vibrations are communicated to surrounding gaseous, liquid,
and solid media in every direction, and at last reach the organs of
hearing. The vibratory movement then acts through the drum of
the ear upon the special nerves of that organ, and produces in
the brain the sensation of sound.

The existence of these sonorous vibrations may be proved by
very simple experiments.

If we take a violin string and stretch it at its two extremities upon
a surface of a darkish colour — this condition is realized in stringed
instruments — and if sound is then produced by the aid of a trans-
verse bow, or by plucking the string from its position of rest, the
string will appear to expand from its two extremities to the middle,
and will here present an apparent enlargement, due to a rapid
alternating movement across its normal position. The string is seen
at the same time, so to speak, in its extreme and in its mean
positions, in consequence of the persistence of luminous impressions
on the eye. (Fig. 102.)

146 PHYSICAL PHENOMENA. [BOOK n.

Instead of a string, let us imagine a cane or a flexible metallic rod
fixed at one of its ends. On moving it from the position of rest, it
undergoes a series of oscillations, the amplitude of which continues
to decrease until at last the motion ceases. During the vibrations
of the rod, a sound is heard which decreases and ends with the
movement. (Fig. 103.)

The rim of a glass or metal bell, rubbed with a bow, emits
sounds which are frequently very loud.

FIG. 102.— Vibrations 01 stretched string.

The existence of the vibrations which induce these sounds is easily
proved. If we take a rod of metal the point of which grazes the rim of
a glass bell without touching it, when the bell vibrates the rod strikes
the glass with sharp and repeated strokes, and the noise thus produced is
quickly distinguished from the sound produced by the bell. (Fig. 104.)
The ball of a pendulum is also sent back with force, and oscillates
during the time that the sound continues. In the same way a
metallic ball placed in the interior of a bell moves about when
this latter is caused to resound, as in Fig. 105, and thus proves the
existence of the vibrations with which the molecules of the sounding
body are animated.

CHAP. IV.]

SONOROUS VIBRATIONS.

147

Trevelyan's instrument, of which we have spoken before, and
by the aid of which sounds are obtained by the contact of two solid
bodies at unequal temperatures, also proves the existence of the
vibrations which produce sounds. If we place a bar terminated by
two knobs on the heated metal, the weight of this bar renders its
vibrations slower, and we can watch the alternating motion of
the rod and knobs. (Fig. 106.) Tyndall has devised an ingenious

FIG. 103. — Vibrations of a metal rod.

way of showing these vibrations. He fixes at the centre of the
vibrating metal a small disc of polished silver, on which a beam of
the electric light is cast. The light is reflected from the mirror to a
screen, and as soon as the warm metal comes in contact with the cold
lead, the motion of the spot of light is apparent on the screen. When
we study the effects of heat, we shall observe that the cause of the
oscillations of the metal, in Trevelyan's instrument, is the alternate
dilatation of the lead at the points of contact of the warm metal ; this

148

PHYSICAL PHENOMENA.

[BOOK IT.

dilatation produces small nipples/ which, by their rising, throw the
heated rocker from side to side, and this alternating motion takes
place with sufficient quickness to produce vibrations in the air, which
reach our ears as sound. (Fig. 107.)

We shall presently see other proofs of the existence of these mole-
cular movements, when we describe the processes used to measure the
number of vibrations produced by sounding bodies. When a solid

FIG. 104. — Proof of the vibration of a glass bell.

body produces a sound, the vibratory movement is readily rendered
perceptible by the trembling communicated to the hand on touch-
ing it. The vibrations of liquids and gases, when they produce or
transmit sound, can also be rendered visible.

A glass goblet, half filled with water, vibrates like the glass bell of

which we have spoken, when the edges are rubbed either with the

'wet finger or with a bow. (Fig. 108.) We observe also on the surface

of the liquid a multitude of waves, which are divided into four and

CHAP. IV.]

SONOROUS VIBRATIONS.

143

sometimes into six principal groups, and these waves become more
serrated as the sound becomes more sharp. If the sound is greatly

FIG. 105.— Vibrations of a metal clock bell.

intensified, the amplitude of the vibrations becomes so great that the
water is jerked from each section in the form of fine rain. Lastly, if

FIG. 106. — Treveiyan's instrument.

we connect a sonorous tube with a pair of bellows, we can prove the
vibration of the interior column of air in the following manner. A

150

PHYSICAL PHENOMENA.

[BOOK ii.

frame covered with a membrane is suspended by a string in the interior
of the tube ; when the tube is caused to emit a sound, we perceive the

grains of sand which previously were at
rest on the membrane to be jerked up ;
thus proving that the vibrations of the
gaseous column have been transmitted
to the membrane itself and to the light
grains which rested upon it. (Fig. 109.)

Vibrations transmitted by the air sometimes possess great power.
Window-panes shake and are sometimes even broken in the neigh-
bourhood of a very loud report, such as that of a cannon.

FIG. 107. — Trevelyan's instrument. Cause
of vibratory movements.

FIG. 108. — Vibrations of liquid molecules.

We have thus demonstrated by experiment the fundamental fact
that sound results from a vibratory motion produced by the molecules
of solid, liquid, or gaseous elastic bodies, which vibrations are trans-
mitted to the organ of hearing by the intervention of different media

CHAP. IV.]

SONOROUS VIBRATIONS.

151

which extend between the sonorous body and the ear. We now
understand why sound is not propagated in a vacuum. The bell
struck under the receiver of the air-pump vibrates freely, but its
vibrations are no longer transmitted, or at least are very imperfectly
transmitted, by the cushion which supports the instrument, and by
the small quantity of air which always remains in the most com-
plete vacuum which it is possible to produce by an air-pump.

We shall endeavour shortly to give some
idea of the nature of sonorous vibrations, and
of the successive condensations and dilatations
which result from their propagation through
elastic media, in order to explain how the
laws of acoustics, which all our observations
and experiments confirm, have been proved
by theory. For the present we shall con-
tinue to describe phenomena.

Sounds are distinguished from each other
by several characteristics, which we shall
next describe.

The most important of these, not so much
from a physical as from a musical point of
view, is the " pitch," that is to say, the degree
of acuteness or of graveness of sound. Every
one can distinguish acute from grave sounds,
whatever may be the sonorous body which
produces them. Two sounds of the same
pitch are said to be in unison. The intensity
of a sound is quite different from the pitch ; Flo m_vibrations of a gaseous
the same sound can be loud or feeble, with-
out ceasing to have the same degree of acuteness or of graveness.

Lastly, different sounds are distinguished from each other by their
quality, or " clang-tint," as Tyndall proposes to call it (timbre, French;
klangfarbe, German). When a flute and a violin, for example, emit
the same musical sound with equal force, the ear will not fail to
distinguish a difference between the two sounds, such that it will be
impossible to confound them. It is this peculiar quality by which
we recognise the sound of a voice which is familiar to us.

The pitch of a sound depends on the greater or smaller number of

152

PHYSICAL PHENOMENA.

[BOOK ii.

vibrations which are produced by the sonorous body and propagated
through the media by the help of which sound is conveyed. This
number increases as the sound becomes more shrill, and we shall
now see by what means philosophers have proved this important fact,
and how they have counted the movements, which the eye or our other
senses could only have observed in a confused and uncertain way.

The toothed wheel invented by Savart enables the number of
vibrations which produce a given note to be determined. The sound
— which to give us a musical note must fall with regular pulsations

FIG. 110. — Savart's toothed wheel. Study cf the number of vibrations producing sounds
of given pitch.

on our ears, irregular pulsations only producing noise — is produced in
this instrument by the teeth of a rapidly revolving wheel striking
against a piece of card. When the velocity of the wheel is small, we
only hear a series of separate strokes, the whole of which, properly
speaking, do not produce a musical note, and the pitch is conse-
quently absent. But in proportion as the velocity of the wheel
increases, the multiplied vibrations of the card transmitted to the
air produce a continuous and regular note, the acuteness of which is
greater as the velocity of the wheel increases. An indicator is fixed
to the toothed wheel, which gives the number of revolutions which it

CHAP. IV.]

SONOROUS VIBRATIONS.

153

makes in a secoud : this number, multiplied by that of the teeth,
gives the half of the total number of vibrations ; for it is clear that
the card, at first bent from its position of rest, afterwards returns on
itself, and produces two vibrations for each tooth which strikes it.

Savart obtained with a whe^l furnished with 600 teeth as many
as forty revolutions a second, and subsequently 48,000 vibrations
in the same time; which corresponds, as we shall see further on,
to a sound of extreme elevation or acuteness.

The Syren, invented by Cagniard-Latour, is also used to measure
(even with greater precision than the toothed wheel of Savart) the
vibrations of a given sound.

FIG. 111. — Cagniard-Latour's Syren.

FKJ. 112.— Interior view of the Syren.

In this ingenious instrument the sound is produced by a current
of air from a pair of bellows, which air passes through a series of holes
placed at equal distances round two metallic plates, one being fixed
and the other movable. When the holes correspond, the current of
air passes, and its force of expulsion acting on the oblique channels
which form the holes, gives movement to the upper plate. This
act causes the coincidence to cease, then establishes it again, then
stops it, and so on, the result being the production of a series of
puffs which produce vibrations, increasing in rapidity, in the air.

154

PHYSICAL PHENOMENA.

[BOOK if.

If there are twenty holes, there are forty vibrations for each turn
of the plate : so that in counting the number of revolutions
which are effected for a given sound in a second, the total number
of vibrations can be easily calculated. The axis of the movable
plate works, by means of an endless screw, in a toothed wheel,
the number of teeth being equal to that of the divisions of a dial
outside. When the wheel advances a tooth, the needle marks one
division ; so that the number of divisions passed over by the needle
gives that of the turns, and then, by simple multiplication, that of the

Fio. 11.!.— Seebeck's Syren.

sonorous vibrations. At the end of each revolution, a catch turns a
second wheel one division ; so that if the first wheel has a hundred
teeth, the needle of the second dial indicates hundreds of turns.

The indicator is disposed so that it only moves at will ; that is to
say. when the attained velocity has produced the note which we
desire to examine as regards the number of vibrations which consti-
tute it. The chief difficulty is to maintain a constant velocity, so as
to have a note of invariable pitch for as long a time as possible.

CHAP. IV.]

SONOROUS VIBRATIONS.

155

The syren also acts in water ; in this case the liquid rushes
through the holes under the pressure of a lofty column of water,
and thus produces vibrations. The sound which follows proves
that liquids enter into direct vibration, like gases, without sound
being communicated to them by the vibrations of a solid. The
name syren comes from the circumstance that the instrument sings
under water like the enchantresses of the fable.

Seebeck's syren, represented by Fig. 113, is constructed in quite
a different manner, but the principle is the same, viz. that the note

Fu;. 114. — Graphic, study of the sonorous vibrations. I'honautography.

is produced by the regular passage of air in puffs through the holes of
a disc. The disc is caused to rotate by clockwork, and the velocity
of its rotation is measured by an indicator. Around it is a wind-
chest communicating with a pair of bellows: and it acts as distributor
of the current which is transmitted by caoutchouc tubing to any
series of holes in the disc which the experimenter may wish to use.

A great number of experiments can be -made with this syren
by varying the number and distribution of the holes in different discs

156

PHYSICAL PHENOMENA.

[BOOK ir.

Lastly, certain graphic methods, recently invented, but the first
idea of which is due to Savart, allow us to determine with exacti-
tude the number of sonorous vibrations.

A tuning-fork, or metallic rod, furnished with very fine points,
may be caused to trace undulating lines on the surface of a turning

Fro 115.— Cora hinnt'on of two parallel vibratory movements.

cylinder covered with lamp-black. The number of sinuosities thus
marked is that of the vibrations. This method is specially employed
when we wish to compare together two sounds with respect to their
pitch. For example, we fix on a tuning-fork the point which trace?
the sinuous lines, and on a second tuning-fork the plate covered
with lamp-black where these lines are traced. Then causing the two

CHAP. IV.

SONOROUS VIBRATIONS.

157

tuning-forks to vibrate simultaneously, the sinuous line obtained will
be evidently the result of the combination of two vibratory move-
ments, parallel if the two tuning-forks vibrate in the same direction,
rectangular if they vibrate at right angles. Figs. 115 and 116 are
facsimiles of proofs obtained by these two combinations for various
musical intervals.

The various experiments which we have just described tend t
prove that the pitch of a sound depends only on the i
vibrations executed by the sonorous body in a given time.

Fio. 116. — Combination of two rectangular vibratory movements.

intensity of the sound, whether strong or feeble, undergoes no change ;
the nature of the sonorous body and the particular quality, which is
called the clang-tint, has likewise no influence on the number of
vibrations.

The amplitude of the vibrations gives to sound greater or less in-
tensity, as may be proved by many familiar experiments. When a bow
is drawn across the string of a violin, or of any other similar instru-
ment, the sound decreases in proportion as the vibration of the cord
is less considerable. The more vigorous the friction of the bow. the
more marked are the oscillations, and the greater the intensity nf
the sound. Since, then, its pitch is not modified, we must conclude

158 PHYSICAL PHENOMENA. [BOOK it.

that the number of vibrations is not altered, although the motions
of the cord are made with greater rapidity, the path traversed in an
equal time being greater when the amplitude is itself greater.

When an elastic body produces a sound, the molecules of which it
is composed are not equally moved from their positions of rest : there
are some even, as we shall soon see, which remain in a state of repose.
A bell, for example, when struck by a hammer, is caused to become
elliptic, first in one direction, then in another at right angles to the
first. The zones of metal at its base execute slower vibrations and
of greater amplitude than the zones near the top. But the solidity of
the zones or rings produces a compensation between these amplitudes
and the different velocities, and there results for the sound produced
a mean pitch and intensity which depends on the dimensions and
nature of the metal of which the bell is formed. This indicates an
evident analogy between these vibrations and the oscillations of the
compound pendulum, the length of whjch we have seen is a mean
between the lengths of the oscillations of a series of simple pendulums
of different lengths.

The above remarks relate only to the intrinsic intensity of sound,
which depends on the amplitude of the vibrations executed by the
moving molecules. But as sound is transmitted to our ear through
the medium of the air, the intensity will be greater as the volume of
air displaced at the same time is more considerable, and conse-
quently the dimensions of the sonorous body will themselves be
greater. A string stretched on a straight piece of wood gives a
weaker sound than if it were stretched on a sounding-board, as in
musical instruments, the violin, piano, &c. Most people know that if
a tuning-fork is caused to vibrate first in the air, and then placed on
a table or on any other elastic body, the sound acquires, by this
increase of volume of the vibrating body, a much stronger intensity.

The intensity of a sound received by the ear at different distances
decreases in the inverse ratio of the square of the distance. Thus,
at 10 yards the intensity is four times greater than at 20 yards, nine
times more than at 30 yards, &c. provided that the circumstances of
the propagation remain the same, and that reflecting bodies are not
present to strengthen the sound. Hence it follows that if two sounds,
one being four times louder than the other, are produced at two
different stations, the observer who is placed at a distance from the

CHAP, iv.] SONOROUS VIBRATIONS. 159

weakest of them, one-third of the whole distance which separates them,
will believe that he hears two sounds of the same intensity.

The reason is as follows : — Sonorous waves are propagated spheri-
cally around the centre of disturbance, hence the vibrations put into
movement successive spherical shells, the volume of which is in pro-
portion to the surface, and therefore increases as the squares of their
distances from the centre. Since the masses of the dispersed layers
are greater and greater, the movement which is communicated to
them by the same force must diminish.

In columns, or cylindrical tubes, the successive impulses are equal :
the intensity of the propagated sounds must therefore remain nearly
the same, whatever the distance may be. This is also confirmed by
observation. M. Biot, in the experiments by which he determined
the velocity of sound in solid bodies, proved the fact, that the sound
transmitted by the air in the pipes of the aqueducts of Paris
was not sensibly enfeebled at a distance of nearly a kilometre.
Two persons speaking in whispers could easily hold a conversation
through these pipes. "There is only one means not to be heard,"
says M. Biot, — "not to speak at all."

Speaking-trumpets and acoustic tubes are applications of this
property which we have just described. We shall speak of some
of these hereafter.

This property of cylindrical sound channels explains certain
acoustic effects shown in rooms or vaults of different monuments.
The mouldings of the vaults or walls form channels where the sound
is propagated with great facility and without losing its first intensity.
In Paris, there are two rooms of this kind ; one square and vaulted,
situated at the Conservatoire des Arts et Metiers; the other, of a
hexagonal form, in the Observatory of Paris : in both, the angles,
being joined by an arch, form deep furrows, which eminently conduce
to the conduction of sound without enfeebling it. Two persons also
can converse in whispers, from one corner to the other, without the
auditors placed between them being able to hear any of their conver-
sation. In St. Paul's cathedral the gallery of the dome affords a
similar instance: the gallery of Gloucester is another example, the
cathedral of Girgenti in Sicily, and the famous grotto of Syracuse, at
t he present day known as the " Grotta della Favella," and in olden
times as that of the Ear of Dionysius. It was in the ancient Latomiae,

160 PHYSICAL PHENOMENA. [BOOK n.

or quarries of Syracuse, that the Tyrant had contrived a secret com-
munication between his palace and the caverns where he kept his
victims, taking advantage of the peculiar arrangement of the grotto
to listen to their conversation.

The intensity of the sound perceived varies according to the
density of the medium which propagates it. We have seen this
already, in the experiment made under the receiver of the air-pump .
the sound of the bell is enfeebled in proportion as the vacuum is
increased. The contrary would take place, as Hauksbee has proved,
if the air were compressed in the receiver wherein the sonorous
body is placed. Persons who ascend into the high regions of the
air, either on mountains or in balloons, all notice the gradual
decrease of sound due to the diminution of the density of the
atmospheric air. In water, the sonorous waves are transmitted with
greater intensity than in air, if the sonorous body vibrates with
the same energy in both media. In solid bodies of cylindrical or
prismatic form, sound is propagated without being enfeebled as much
as in the air or other gases. We most of us know the experiment
of placing the ear at the end of a long wooden beam, when we
can hear very distinctly the slightest noise — for example, that pro-
duced by the friction of a pin. Savages place the ear near the
ground to hear distant sounds which could not be transmitted by
the air through the same distance.

It is a fact generally known and of easy observation, that sound is
heard further during the night than during the day. This increase of
intensity is attributed to the homogeneity of the strata of air and
their relatively calm condition, which allows the sonorous waves to
be propagated without losing their energy by reflection. It must
also be remembered that during the day various noises conduce at
the same time to make an impression on the ear, each of which must
be less easily distinguished. According to the observations of Bravais
and Martins, the distance to which a sound reaches depends also on
the temperature of the air : this distance is greater during the cold of
winter, in snowy regions of the pole, or high mountains. Here it is
to the homogeneity of the air rather than to its density that we
must attribute this result, for on the summit of mountains
the density of the air is less than in the plains. The intensity
of transmitted sound certainly depends on the state of repose or

CHAP, iv.] SONOROUS VIBRATIONS. 161

agitation of the air. In calm weather it is distinctly heard at
great distances : wind enfeebles sound even when it comes from the
point where the body gives out the sounds. The direction of the
vibrations, that is to say, the manner in which the auditor is turned
relatively to the point whence the sound starts, has also a great
influence on its intensity. When we hear the flourish of a hunting
horn, if the performer turns the mouth of his instrument in different
directions the intensity varies, so that it seems sometimes to get nearer
to and sometimes further away from the hearer.

The circumstances which tend to modify the intensity of sound
are thus very varied. It is therefore difficult to determine the
greatest distance to which it can reach. In the remarkable examples
which are quoted, of sounds heard at considerable distances, it is
probable that it is the ground rather than the air which serves as
a vehicle to the sonorous vibrations. We have already quoted
Humboldt on the subject of the reports produced by earthquakes and
volcanic eruptions, which are propagated to distances of 500 to 800
miles. Chladni relates many facts which prove that the noise of
cannon is often heard at very great distances ; at the siege of Genoa
it was heard at ninety miles from Italy ; at the siege of Mannheim
in 1795, at the other side of Swabia, at Nordlingen and Wallerstein ;
at the battle of Jena, between Wittenberg and Treuenbrietzen. " I
have myself heard," he says, " cannon-shots at Wittenberg at seventy-
five miles, not so much by the air as by the disturbance of solid
bodies, by placing the head against a wall."

Nevertheless, sound, such as the rolling of thunder and the detona-
tions of meteors, which sometimes burst at enormous heights, is often
propagated to a great distance by the air. Chladni mentions certain
meteors the explosion of which was not heard until ten minutes after
the luminous globe was seen : this supposes a height of not less than
120 miles. The bolide observed in the middle of France on the
14th of May, 1864, presented the same peculiarity, and the observers
calculated four minutes between its appearance and their perception
of the noise of its report. " Since the explosion," says M. Daubre*e,
writing on this subject, " is produced in strata of air highly rarefied,
the fact that it gives rise on the surface of the earth to a noise of such
intensity, and over a horizontal extent so considerable, demonstrates
that its violence in high regions exceeds all that we know." Unless,

162 PHYSICAL PHENOMENA. [BOOK n.

indeed, this should be an effect of repercussion of the sound on
strata of air of unequal density, analogous to the rolling of thunder
in storms.

We know hut little at present of the production of the indefinite
varieties of tones. We shall speak hereafter of recent researches
on this subject ; the phenomena which we must first notice are
necessary for the right understanding of the proposed explanations.

Experimenters have tried to determine the limit of perceptible
sounds ; but it is clear that this limit depends partly on the sensibility
of our organs. The gravest sound appears to be that which is pro-
duced by a sonorous body executing thirty-two simple vibrations in
a second. Savart found for the most acute, 48,000 vibrations. But
M. Despretz made a series of tuning-forks the sounds of which were
strengthened by resonant boxes, and he at last distinguished the
sound of greatest sharpness which a tuning-fork can produce to be
caused by 73,700 vibrations per second. Such shrill sounds produce
in the organ of hearing a sensation almost painful.

CHAP, v.] LAWS OF SONOROUS VIBRATIONS. 163

CHAPTER V.

LAWS OF SONOROUS VIBRATIONS, IN STRINGS, RODS, PIPES, AND PLATES.

Experimental study of the laws which govern the vibration of strings — Monochord
or Sonometer — Nodes and ventral segments ; harmonics — Laws of the vibra-
tions of sonorous pipes — Vibrations in rods and plates — Nodal lines of square,
round, and polygonal plates.

IN the present day, the art of music is so generally understood
that those of our readers who have knowledge of it, or who have
seen it produced, know the mechanism of stringed instruments, such
as the violin.

Four strings of unequal diameter and of different textures are
stretched between two fixed points by the aid of pegs, and when
caused to vibrate, either by the hand or by drawing a bow across
them, they produce sounds of different pitch. The sounds produced
by the fully opened out strings (that is to say, when they vibrate in
the whole of their length) must have a certain connection of tone
between them. When this connection is destroyed, the instrument
is not in tune. What does the musician then do ? By screwing
and unscrewing the pegs he stretches or slackens those of the
strings which do not give out the desired sounds : as he tightens
them the sound becomes more acute; on the other hand, if he
loosens them it becomes more grave. But four sounds would not
be sufficient to provide all the varied notes of a piece of music.
The performer multiplies the number at will, by placing the fingers
of his left hand on certain points of each of the strings. In doing
this he reduces to different lengths the portions of these strings
which the bow causes to vibrate.

These facts show that certain relationships exist between the
pitch of the different sounds given out by the instrument and

o 2

104 PHYSICAL PHENOMENA. [BOOK n.

the length, diameter, tension, and substance of the strings; as the
pitch itself depends on the number of the vibrations executed,
it necessarily follows that this number is connected by certain
laws with the elements already mentioned. Some of the most im-
portant were noticed by the ancient philosophers, and particularly
by the Pythagoreans. But it is to the geometers of the last century,
amongst whom are the illustrious names of Taylor, Bernouilli,
D'Alembert, Euler, and Lagrange, that we owe the complete demon-
stration deduced from purely theoretical reasons. The exactness of
the calculations has been confirmed by experiments.

We shall now endeavour to explain these laws. In the present day
they are readily proved by means of a peculiar instrument, called
a monochord or sonometer, to which is attached an apparatus which

FIG. 117. — Sonometer.

enables us to ascertain the numbers of vibrations produced. The
sonometer, or monochord (Fig. 117) is formed of a box of fir-wood
to strengthen the sound ; above this box one or several strings are
fixed at their extremities by iron pins, and stretched by weights
which serve to determine the tensions of each of them. A divided
scale beneath the strings shows the lengths of the vibrating parts
which can be altered at will by the aid of a movable bridge which
moves along the scale under the strings.

Let us take a string of catgut or metal, and stretch it by a weight
sufficient to cause it to produce a perfectly pure sound, of a
pitch appreciable to the ear; and let us suppose that its total
length measured by the scale is 1-20 metre, and that the sound which
it gives out corresponds (as verified by the Syren) to 440 vibrations

CHAP, v.] LAWS OF SONOROUS VIBRATIONS. 165

a second. Let us place the movable bridge first at the half, then at
J, \, and TV of the total length; and in each of these successive
positions let us cause the shortest portion of the string to vibrate.
Measuring the different sounds obtained, we shall find the following
number of vibrations a second: 880, 1,320, 1,760, and 5,280.

It only remains for us to compare the numbers which indi-
cate the different lengths of the string, and those which indicate the
number of vibrations, to discover the law.

T ., ,. , • ( 120 60 40 30 10

Length of string . . . ] , , L ± T

z 3 4 TiJ

«t ••-<! r -i ,- • ( 440 880 1,320 1,760 5280
N umber of vibrations . < , ^ ' , ' ^

Is it not evident from this experiment that the number of
vibrations goes on increasing, so that their ratios are precisely the
inverse of those which the lengths of the strings form between them-
selves ? Such is ihe first law of vibrating strings.

Kow, without altering the length, if we stretch the same string by
different weights, and compare the sounds obtained, we shall find, for
the numbers of double, triple, or quadruple vibrations, that the tensions
of the strings are 4, 9, 16, &c. times greater. The numbers of vibrations
follow the order of the simple numbers, the weights or tensions follow
the order of the squares of these numbers. This is the second law.

The strings are of cylindrical form. Let us change the diameter
of these cylinders, and compare the sounds produced by two strings
of the same substance, stretched by equal weights and of equal lengths,
but of different diameters. This comparison will be easy with the
help of the sonometer. It will be found that the number of vibra-
tions of these strings decreases when the diameters of the strings
augment, and become precisely 2, 3, 4 .... times less, when the
diameters are 2, 3, 4 .... times greater.

This is the third law of the transversal vibrations of vibrating
strings.

There is a fourth law, which, like the others, may be proved by
means of the sonometer, and which relates to the density of the sub-
stance of which the vibrating string is composed. Two strings, one
of iron, the other of platinum, of the same length and diameter, are
stretched on the sonometer by equal weights. The sounds which

166 PHYSICAL PHENOMENA. [BOOK n.

they will give out will be graver as the density is greater, so that
the iron string will give the acuter and the platinum the graver
sound ; the ear will be sufficient to judge of these differences. Now,
if we measure the exact numbers of vibrations which correspond
to the two sounds obtained, we shall find —

For the iron . . .' ..:"-.;' . ' . . . « . . 1,640
For the platinum 1,000

We riot only speak here of the numbers, but of their relationship.
Now, if we multiply each of these numbers by itself, if we take their
squares, we find 2,699,600 and 1,000,000, which indicates precisely
in an inverse order the densities of the metals, platinum and iron.
The density of iron is 7 '8, that of platinum 21*04, and these densities
are related as I'OO is to 2'69. Such is the law : other things being
equal, the squares of the number of vibrations are in the inverse
ratio of the densities of the substances of which the vibrating strings
are formed.

In the preceding remarks we have spoken only of the transverse
vibrations of strings, that is to say, of the sounds which follow either
from the plucking or removing a string from its position of rest, or
from drawing a bow across it. A string rubbed lengthways with a
piece of cloth powdered with resin also emits a sound, but this sound
is much more acute than when it vibrates transversally, so that the
number of the longitudinal vibrations always exceeds that of the
transversal vibrations. As this method of causing strings to vibrate
is not employed, we need not enlarge on the subject. But we must
not conclude the discussion of vibrating strings without mentioning
a phenomenon of great interest : that of nodes and ventral segments,
and of the particular sounds which musicians and physicists call
harmonics. Imagine a string stretched on the sonometer, or on any
musical instrument, and let it be fixed by placing a finger at the
middle. Then cause one of the halves to vibrate by means of the
bow : the sound produced will be more acute than the fundamental
sound — that is, the sound given out by the string when its whole
length vibrates — the number of the vibrations being exactly
doubled. Musically speaking, this is the octave of the fundamental
note. But it is remarkable that the two halves of the string vibrate
together. The fact may be proved, first by putting crosswise on

CHAP, v.] LAWS OF SONOROUS VIBRATIONS. 167

__^_______ »

the centre of that half of the string which remains free a few little
paper riders, which will jump about and fall directly the sound is
produced ; secondly, by demonstrating to the eye the existence of an
enlargement in the two halves of the string (Fig. 118; ; for if we
remove the finger without stopping the movement of the bow, we
notice that the sound continues, as well as the division of the string
into the two parts, which still vibrate simultaneously.

Let us make a second experiment, and place the finger on a portion
of the string one-third of its entire length from the nearest bridge,
continuing to draw the bow across the smallest portion (Fig. 119).

FIG. 118. — Harmonic sounds. Nodes and ventral segments of a vibrating string.

The sound is even more acute, and we observe that the whole string
is divided into three equal parts, vibrating separately : this can be
proved by placing the riders at the points of division, as well as
at the middles of each third of the string. The first remain im-
movable, the others are thrown off; which proves the existence
of immovable points or nodes, and vibrating parts or ventral
segments. Against a black ground, the nodes and ventral segments
can be clearly distinguished. The first are where the white string

168

PHYSICAL PHENOMENA.

[BOOK n.

is reduced to its proper thickness ; the others where we see swellings
similar to those which we have before noticed at the centre of a
string vibrating as a whole.

A string can thus be divided into 2, 3, 4, 5 .... equal parts,
and the sounds, gradually increasing in acuteness, which these
parts produce, are called harmonics. Practised ears can distinguish
some of the harmonic sounds which are produced simultaneously
with the fundamental sound of a string, which proves that the
division of the string into vibrating portions takes place even when

FIG. 119. — Harmonics. Nodes and ventral segments of a vibrating string.

the contact of a point is not the determining cause. Further on
we shall see the position which these different sounds occupy
in the musical scale. Studied by the help of the graphic method,
the sonorous vibrations which engender harmonics show that they
result from compound sounds superposed on the simple vibrations
(Fig. 120). Nodes and ventral segments are not peculiar to
vibrating strings : we shall find them also in the columns of
air which vibrate in the interior of pipes and in plates and
membranes.

CHAP, v.] LAWS OF SONOROUS VIBRATIONS. 169

Musical instruments called wind-instruments are formed of solid
pipes, sometimes prismatic and sometimes cylindrical, some straight,
others more or less bent. The column of air which these instruments
inclose is caused to vibrate by means of a mouthpiece, the form and
disposition of which varies according to the nature of the instruments.
We shall take occasion to describe the principal instruments when
we treat of the Applications of Physics. But in order to under-
stand the general laws which regulate the vibration of air in
pipes, we shall confine ourselves here to the consideration of
straight pipes in the form of prisms or cylinders, such as exist in
organs. Figs. 121 and 122 represent the exterior view and the sec-
tion or interior view of two pipes of this kind. At the lower part
of each of them we can see the pipe through which the air supplied
by the bellows is made to enter : the current first rushes into a box,

FIG. 120. — Vibrations of compound sounds.

•

thence issues by a chink which is called the mouth of the pipe, and
finally rushes against the edge of a bevelled plate. A part of the
current escapes by the mouth at the outside of the pipe ; the other
part penetrates into the interior. This rupture of the current gives
rise to a series of condensations and dilatations which are propagated
in the column of air. The air of this column enters into vibration
and produces a continuous sound, the pitch of which, as we shall see,
varies according to certain laws. The mouthpiece which we proceed
to describe is that which is called the flute mouthpiece. Experiment
proves that if we substitute in the same pipes mouthpieces of
different forms, it will only modify the quality of the sound without
changing its pitch. The pitch does not depend on the substance,
wood, ivory, metal, glass, &c., which composes the tube, and it

170

PHYSICAL PHENOMENA.

[BOOK ii.

must be concluded that the sound results only from the vibrations
of the column of air.

The science of acoustics owes the discovery of the laws which
govern the vibrations of sonorous tubes to Father Mersenne and
Daniel Bernouilli. Let us briefly indicate the simplest of these
laws. Father Mersenne showed that if we compare the sounds
produced by two similar pipes of different dimensions — that is,

FIG. 121. — Prismatic sonorous pipes.

FIG. 122 — Cylindrical sonorous pipes.

if the one has all its dimensions double, triple, &c., those of the
other — then the number of vibrations of the first will be 2, 3 ....
times less than the vibrations of the other. Thus the smaller of the
pipes represented in Fig. 123 will give twice as many vibrations as
the other : the sound given out will be the octave of the sound of
the largest pipe.

Such pipes are sometimes open, and sometimes closed at
their upper end. But the law which we are about to mention
applies both to open and to closed pipes, provided that their

CHAP, v.] LAWS OF SONOROUS VIBRATIONS. 171

length be great compared to their other dimensions. It must be first
observed that each pipe can produce many sounds, acuter or
higher as the current of air is greater. The gravest of these sounds
is called the fundamental ; the others are the harmonics ; and it is
found that, to obtain them, it is sufficient progressively to force in
the current of air. When tubes of different lengths are caused
to sound, the longest produce the gravest fundamental sounds, in
such a manner that the numbers of vibrations vary precisely
inversely as the lengths. For example, whilst the smallest of the
four tubes represented in Fig. 124 gives 12 vibrations, the other
three give in the same time 6, 4, and 3 ; or 2, 3, 4 times less ; the
lengths being, on the contrary, 2, 3, 4 times greater. As we said before,
this law is applicable to open as well as closed tubes. But, for the

FIG. 123.— Tubes of similar forms.

same length, the fundamental sound of a closed tube is different
from the sound given by an open one. The vibrations are half
as many ; in other words, the fundamental sound of a closed tube
is the same as that of an open tube double the length.

It only remains for us to speak of the succession of the har-
monic sounds in both of them. Arranging these sounds in order,
from the gravest to the most acute, starting from the fundamental
note, we find that in open tubes the number of vibrations increases
according to the series of whole numbers, 1, 2, 3, 4, 5, 6, &c. In closed
tubes, the numbers increase according to the series of the odd
numbers, 1, 3, 5, 7, &c. From this it results that if we take three

172

PHYSICAL PHENOMENA.

[BOOK ii.

tubes, the open one of double the length of the two others, and if, of
these, one is open and the other closed, the successive sounds of the
first will be represented by the series of natural numbers —

Long open tube ..1 2 3 4 5 6 7 8...
and the sounds of the others by

Short open tube . . . 2 ... 4 ... 6 ... 8
„ closed tube . 1 ... 3 ... 5 ... 7 ...

that is to say, the sounds of the large tube will be reproduced alter-
nately by the two tubes of half the length.

FIG. 124.— Sonorous tubes. Laws of the vibrations of open and closed tubes
of different lengths.

We conclude the study of the phenomena presented by sono-
rous tubes by stating that the columns of air which vibrate in

CHAP, v.] LAWS OF SONOROUS VIBRATIONS. 173

the interior of them are divided, like vibrating strings, into fixed por-
tions or nodes, and vibrating parts or ventral segments. The existence
of these various divisions is proved in many ways. The most simple
consists in lowering into the tube by a string a membrane stretched
over a ring, and then watching the grains of sand with which it is
sprinkled. These grains will be agitated under the action of the
vibration, when the membrane reaches a ventral segment in any
portion of the vibrating column of air. On the other hand, they
remain at rest when the position of the membrane coincides with
that of a node.

However, theory has completely solved all the problems which
relate to this order of phenomena : and the experiments of physicists,
always a little less exact than mathematical analysis would require,
on account of the complex circumstances under which they are per-
formed, are only verifications of the laws found by analysis. We,
who wish especially to describe the curious facts of each part of
physics, must confine ourselves to the notions indispensable to the
understanding of these facts and their application to industry
and the arts.

Sonorous rods are cylindrical rods of wood, metal, glass, or any
other elastic substance, which can be caused to vibrate, either by
rubbing them longitudinally with a piece of cloth sprinkled with
resin, or with a damp flannel. They then give out pure and con-
tinuous sounds, the pitch of which for one and the same substance
depends on the length of the rod. By the aid of a vice or with
the fingers, we grasp the rod, either at one of its extremities or at
the middle, or at any intervening part of its length : it is then free
at its two ends, or only at one (Fig. 125). Now, if we compare the
sound which a rod gives out when fixed at one of its extremities, with
that which the same rod or a rod of the same length and substance
gives out when fixed at its middle part, we find that the first is
graver than the second: the vibrations in the latter are twice as
numerous.

If rods of different lengths fixed in the same way are caused to
vibrate, experiment shows that the sounds become sharper as the rods
are shortened. The number of the vibrations which constitute these
sounds varies in inverse proportion to their length. The vibrations

1 74 PH YSICAL PHENOMENA. [BOOK n.

of rods are also governed by the same laws as those of sonorous tubes ;
and we see that if rods free at both ends are compared with open
tubes, the rods fixed at one end correspond to closed ones. The
rod, like the tube, gives out harmonic sounds besides the funda-
mental note, the ascending series also following the same laws as in
the open and closed tubes.

An account of the phenomena which result from sonorous vibra-
tions in bodies of varied forms would be endless. We shall confine
ourselves to the consideration of those which are produced in plates
and membranes. If we cut square, circular, or polygonal plates
out of thin wood or homogeneous metal, and fix them solidly to a
support at their centre of figure, we obtain very different sounds

FIG. 125. — Longitudinal vibrations of rods.

from them if we draw a bow across their edge according as we place
one or two fingers at certain points of their contours (Fig, 126).
Chladni and Savart, whose names are so often to be found in the
story of modern research, and who made sound their special study,
made numerous experiments on the vibrations of plates of different
forms, thicknesses, and surfaces. The phenomenon to which they
particularly drew attention was the division of the plates into vibrating
and fixed parts. These latter, being nothing else but a continuous
series of nodes, were therefore called nodal lines.

To understand and study the positions and forms of these lines,
these two physicists sprinkled the surface of the plate with dry
and fine sand. As soon as the plate entered into vibration, the
particles of sand began to move. They deserted the vibrating parts
and arranged themselves along the nodal lines, thus producing certain
figures or outlines. These lines are often so numerous and compli-
cated, for the same plate they vary so much with the different sounds

CHAP. V.]

LAWS OF SONOROUS VIBRATIONS.

175

which this plate gives out, that Savart was obliged to use a particular
method to obtain them. Instead of sand, he employed litmus powder,
and by means of a damp paper laid on the plate he obtained the
impression of each figure. We reproduce, in Figs. 127 and 128, a
series of nodal lines obtained by Savart and Chladni, and we may
remark that the figures which contain the most numerous lines
correspond to the more acute sounds ; in other words, in pro-
portion as the sound gets higher, the extent of the vibrating
parts diminishes.

In square plates, the nodal lines take two principal directions,
some parallel to the diagonals, the others parallel to the sides of the

FIG. 126.— Vibrations of a plate.

plate (Fig. 127). In circular plates (Fig. 128) the nodal lines place
themselves either in rays or concentric circles. Bells of glass or
metal, and vibrating membranes, are also divided into vibrating parts
and nodal lines, as is seen in the experiment of a glass filled with
water, represented by Fig. 108. Fig. 129 shows two modes of vibra-
tions of a bell, and the way in which it divides itself into four or
six vibrating parts, separated by as many nodes. The first division is
obtained by touching the bell in two points distant about a quarter of
a circle : the bow is then drawn at about 45 degrees from one of the
nodes. The resulting sound is the lowest, and is the fundamental note

176

PHYSICAL PHENOMENA.

[BOOK ii.

ot the bell. The other division is obtained by placing the bow at
a point distant about 90 degrees from the node which is formed by the
touch. The bell would be again divided into 8, 10, 12 vibrating parts.
It is the same with membranes stretched on frames, which are caused
to vibrate by placing near them another sonorous body — for example,

IPfc^

1 ' ' fC'

^X^:"M (; >- :->(':>, ; V }V: :
-./^XN ''* « l\^'\!/\.;,- K / r/! bir-'/Sv^XN^]

- £ 1

\ x-~^,

/ Vv— -•

^q !• . •

-~y\ i AH 1

l/V i • ! .-1 /Xj [/"

•(-^--^'--

~^\ \ '• '' ' ' :
&3U U"';^-'"^--'0^ L-'--./;'- •- "'•.- -\

/ .,\x..,v.-: >:^

FIG. 127. — Nodal lines of vibrating square plates, according to Savart.

a sounding bell. The vibrations are communicated by the air to the
membrane, and the sand with which this is covered indicates the
position of the nodal lines.

It is well known that when two plates of the same substance and
similar figure, but of different thicknesses, give the same nodal
lines, the sounds produced vary as the thickness, if the surface is

CHAP. V.]

LAWS OF SONOROUS VIBRATIONS.

177

the same ; that is to say, that the number of vibrations is proportional
to the thickness. If the thickness remains constant, the numbers of
the vibrations are in the inverse ratio of the surfaces.

We do not yet know the law according to which the sounds
produced by the same plate succeed eacli other when the figures

FIG. 128. —Nodal lines of vibrating circular or polygonal plates, according to Chladni and Savart. •

formed by the nodal lines change. We only know that the lowest
note produced by a square plate fixed in the centre is obtained when
the nodal lines are two in number, parallel to the sides, and pass

FIG. 129. — Nodes and segments of a vibrating bell.

through the centre as shown in the first plate (Fig. 127). When the
two nodal lines form the diagonals of the square (as in the first plate
of the second line, Fig. 127), the sound is the fifth of the first one,
•which may be called the fundamental note.

178 PHYSICAL PHENOMENA. [BOOK IT.

CHAPTER VI.

PROPAGATION OF SOUND IN AIR. — SOUND WAVES.

Nature of sound waves ; their propagation in a tube — The wave of condensation
and the wave of rarefaction — Length of sonorous undulations — Propagation
through an unlimited medium ; spherical waves ; diminution of their amplitude
with, the distance — Direction of sound waves— Co-existence of undulations —

Perception of simultaneous sounds ; Weber's experiments.

WE have just seen how the vibrations of sonorous bodies can be
rendered sensible, and how their number can be counted, and
we have proved by experiment the laws of their vibrations in solids
of different forms, and in gaseous, cylindrical, or prismatic columns.

But when a body sounds, the vibrations which its molecules exe-
cute, reach our ear, so as to impress us with the sensation of sound
by a gradual disturbance of the mass of air intervening between
the centre of disturbance and our organs. Tn the absence of this
vehicle, sound is no longer perceived, or at least only in a very
weakened form, after having been propagated through more or
less elastic solid bodies, which establish an indirect communication
between the sonorous body and the ear. Thus the air itself enters
into vibration under the impulse of the movements of the particles
of the sonorous bodies, and it undergoes successive condensations
and dilatations, which are propagated with a constant velocity, when
the density and temperature remain the same, and when the homo-
geneity of the gaseous mixture is perfect. We shall now explain by
what means sonorous waves succeed each other in the air or any other
gas, and how their length can be measured.

Let us suppose that one prong of a tuning-fork is placed in front
of a tube and is caused to vibrate. The vibrations are propa-
gated along the column of air in the tube. We will observe what

CHAP. VI.]

PROPAGATION OF SOUND IN AIR.

179

takes place in the column of air when the prong executes a whole
vibration ; that is to say, leaves its position a" to go to of, and
afterwards to return to a", passing each time by its mean position
a (Fig. 130). This alternating movement is similar to that of the
pendulum, so that the velocity of the prong is alternately increasing
and decreasing according as it gets nearer to or more distant from
the position a. During the movement from a" to a', the air in the
tube, receiving the impulse from the prong, will undergo successive
and unequal condensations, which will be transmitted from one to
the other, and these waves will be carried along the column of air

FIQ. 130. — Propagation of the sonorous vibrations in a cylindrical and unlimited
gaseous column.

FFG. 131.— Curve representing a sound wave.

like the waves along the surface of water. On this point we shall
have more to say presently. These condensations at first increasing
will attain a maximum ; they will then diminish until the vibrating
prong has reached the position a'. At its return from a to a" the
same gaseous layers, returned to their normal density, will dilate by
virtue of their elasticity to fill the space left in the column of air
by the second movement of the fork.

To each complete vibration of the prong, a series of condensations
therefore corresponds : a condensed half- wave ; then a series of dilata-
tions ; a dilated half- wave. Their whole forms a complete sonorous
wave, which passes along the tube.

To represent to the eye the condition of the column of air in the
whole length of a sonorous wave, it has been found convenient to
represent the different degrees of condensation by perpendiculars

p 2

ISO PHYSICAL PHENOMENA. [F.OOK ir.

placed above and at right angles to the direction of the wave, and the
dilatations which follow (Fig. 131), by perpendiculars traced below this
direction : these two lines have a minimum length when the density
is the normal density : their maximum lengths correspond to the
maximum condensations and dilatations. The curve AA"lf A'I} Al
then represents the state of the successive strata of the tube at the
moment when the prong of the tuning-fork has executed an entire
vibration ; AAX is the path traversed during this time, — that is to say,
the length of the sonorous wave.

The space traversed by this wave will be double, triple, &c. after
the 2, 3, . . . . first vibrations.

It is now easy to understand how the wave-length of a sound of a
given pitch can be calculated. Let us suppose a sound produced by
450 vibrations a second. At the temperature of 15° C. — if such is the
temperature of the air at the time of the experiment — as the velocity
of propagation is 340 metres during the same interval, it is clear that
at the moment when the wave reaches this distance, there are in the
air as many successive sound waves as there are complete vibrations
from the centre of emission ; that is, 450. Each of them has then a
length of the four hundred and fiftieth part of the space traversed,
that is, of 340 metres ; hence the length of wave in this case is 755
millimetres. If we pass now from the case in which the sound is
propagated in a column of air to that in which the propagation is
made in all directions emanating from a point, the successive conden-
sations and dilatations of the strata of air will be distributed at equal
distances from the centre of emanation. The waves will be spherical,
without either their velocity of propagation or their length changing.
Only the amplitude will diminish, and consequently the intensity of
sound. Figure 132 will give the reader an idea of the manner in
which sonorous waves are distributed round a centre of emission.
We see the series of condensed and dilated half-waves, and the un-
dulating lines starting from the centre show how the condensations
and dilatations lose their amplitude in proportion as the distance
increases.

To account for the fact that waves are propagated without the parti-
cles of air moving with them, sound waves may generally be compared
to the movement of a cord which is sharply jerked by the hand. The
undulations traverse the cord from one end to the other ; and if it is

CHAP, vi.] PROPAGATION OF SOUND IN AIR. 181

fastened by one of its extremities, the wave returns on itself. In
either case, the movement is transmitted without any real change in
the distance of the molecules from the point whence the impulse is
derived, The same effect is observed when we throw a stone into
water ; the disturbance produced in the liquid mass is propagated in a
series of concentric waves which disappear as the distance increases,
but the molecules of water are not transported, as it is easy to prove

FIG. 132.— Propagation of a sonorous wave through an unlimited medium.

to oneself by observing the fixed position of light substances floating
on the surface. But in these examples, which are otherwise useful in
giving us some idea of the mode of propagation of sound waves,
there is an essential difference which must not be forgotten. The
condensations and dilatations of the air caused by trhe vibrations of
sonorous bodies are effected in the same direction as the movement
of propagation ; they take place parallel to the direction of each

182 PHYSICAL PHENOMENA. [BOOK n.

sonorous wave, whilst the undulations of the cord, or those of the
surface of the water, are effected in a direction perpendicular to the
movement of propagation. We shall soon see that something like
this takes place with the waves which traverse the medium called the
ether, which have their origin in vibrations from luminous sources.

All this perfectly accounts for the transmission of a single sound
which the air carries, so to speak, to our ear. But if the air is thus
the vehicle of sonorous vibrations, how does it happen that it pro-
pagates, without alteration, the vibrations of many simultaneous
sounds ? We are at a concert ; numerous instruments are simulta-
neously emitting sounds which differ in intensity, pitch, and quality.
The centres of emission are distributed over the room ; how is it
that the mass of air inclosed by the walls is able at the same
time to transmit so many vibrations without the production of
complete chaos of sound ?

Or again, it is morning. A fine thick rain falls, and the drops on
striking the ground produce a multitude of little noises which arrive
in a distinct form to our ear ; the songs of birds, which the corning
of spring awakens everywhere, rise in the air, and seem to pierce
the light mist which the rain sheds on the horizon. Above this
warbling, cock-crowing, barking of dogs, jolting of heavy carts on the
paved road, rise the sound of bells, and here and there human voices,
all of which sing, cry, speak, and sound altogether without the ear
finding any confusion. These multiple sounds, the simultaneity of
which arid their resonances would make them discordant if they were
all produced in a narrow space, are drowned in the vast extent of the
stratum of air which covers the plain, and mingle into pleasing har-
mony. Here, the same question presents itself: How can the air
transmit distinctly and at the same time so many undulations
emanating from different centres, so many vibrations which are not
isochronous ? How can the intensity, pitch, and quality of each sound
co-exist, in this elastic and movable medium, without alteration ?

This is a problem the data of which appear so complex, that it is
beyond analysis. Nevertheless, theory accounts for these phenomena,
the explanation of which appears so difficult at first sight, and simple
experiments justify the theoretical conclusions. Two distinguished geo-
meters of the last century, Daniel Bernouilli and Euler, demonstrated
the principle of the co-existence of small movements and oscillations in

CHAP. VI.]

PROPAGATION OF SOUND IN AIR.

183

the same medium. The following is their theory. If we throw into
water two or more stones near to each other, we perceive concentric
circles produced by each of them, which cross without destroying one
another, especially if their amplitude is not too great. Fig. 133, which
we borrow from the work of M. Weber, uber die Wellenlehre, shows
how waves cross each other on the surface of a liquid, and how they
are reflected from the sides of the containing vessel. The form of the

FIG. 133.— Experiment proving the co-existence of waves. Propagation and reflection
of liquid waves on the surface of a bath of mercury.

latter is elliptical, it is filled with mercury, and the waves which are
seen on its surface are those produced by the fall of a drop of the
liquid in one of the foci of the ellipse. Concentric circular waves
are produced at this focus, then reflected waves which all tend to
collect at the second focus of the curve. The same results are evi-
dently produced as if a drop had fallen at the same time at
the other focus.

184 PHYSICAL PHENOMENA. [BOOK ir.

This ingenious experiment proves, then, on the one hand, the
possible co-existence of waves, and, on the other, the law of their
reflection. After the reservation of which we have spoken above
as to the direction of sound waves, we thus obtain a very good
idea of the reflection of sounds and their simultaneous propagation
through the air.

CHAP. VIT.] MUSICAL SOUNDS. 18'

CHAPTER VIT.

MUSICAL SOUNDS. — THE GAMUT, OR MUSICAL SCALE.

Distinction between noises and musical sounds— Definition of the gamut; intervals
which compose it — The scale of the musical gamut is unlimited ; convention
which limits it in practice — Names and values of the intervals of the natural
major scale — Modulations ; constitution of the major gamuts proceeding by
sharps and flats — Minor scale.

THE human ear, as we have remarked in the preceding chapter, is
limited as regards its perception of sound. It has been proved
by experiment that 32 simple vibrations per second is the limit of
grave sounds, while that of acute sounds is 73,000 vibrations. Between
these extreme limits the scale of sounds is evidently continuous, so
that there is an infinity of sounds having a different pitch appre-
ciable to the ear, and passing from the grave to the acute, or from
the acute to the grave, by imperceptible degrees.

All the sounds comprised in this scale, and susceptible conse-
quently of being compared among themselves as regards pitch, are
what are called musical sounds; by combining them by means of
succession or simultaneity, according to determined rules of time,
pitch, intensity, or quality, the musician is able to produce the effects
which constitute a musical composition.

Are all the sounds and noises perceptible to the ear, musical
sounds ? Undoubtedly not, if we mean by musical sound that which
a composer or artist thinks right to introduce into his work to add to
the desired effect. Not only must these sounds be closely connected
by bonds which are determined by the pitch, but they must also
unite certain particular qualities the examination of which belongs
to the domain of art rather than of science. The question becomes
altered if the term musical sound is applied exclusively to those
whose pitch is appreciable, and which the ear can compare to other

186 PHYSICAL PHENOMENA. [BOOK n.

higher or graver sounds, the vibrations of which may be measured
according to a constant and regular law. In this case, physicists dis-
tinguish noises properly so called from musical sounds. Noise fre-
quently proceeds from a confused mixture of different sounds which
the ear can scarcely distinguish from each other, but the separation of
which is possible. At other times, noise is nothing but a sound the
vibrations of which do not last long enough to enable the hearer to
appreciate the relative pitch. The cracking of a whip, the collision of
two stones or two pieces of wood against each other, and generally of
any two bodies which are but weakly sonorous, the report of fire-arms,
are noises of this last kind ; whilst the dull surging of a stormy sea
and the rustling of leaves in a forest proceed from the mixture of
a multitude of sounds or confused noises.

The attempts which have been made to compare the pitch of simple
noises with musical sounds prove that the distinction of which we
speak is more apparent than real. Physicists have succeeded, by
varying the dimensions of a series of wooden balls and causing them
to come together in collision, in making them emit the tones of the
musical gamut ; but, in order that the ear should easily seize their
relationship, it is necessary that the sounds succeed each other at very
short intervals. On the other hand, we can separate the noises formed
of sounds mixed together, and can distinguish some of the elementary
sounds of which these noises are composed. The sensibility of the ear,
joined to the habit of comparisons of this kind, contributes greatly to
render these distinctions possible.

Let us now endeavour to form some idea of the succession and con-
nection of sounds which constitute musical scales known under the
name of gamuts and which form the physical basis of modern music.

The name of " gamut " is given to a series of seven sounds which
succeed each other, proceeding from the grave to the acute, or from the
acute to the grave, and which are comprised between two extreme
notes having the following character, viz. that the highest sound is
produced by double the number of vibrations of the lowest. The
most acute note being the eighth of the series, the two extreme notes
are the octaves of each other : one being the lower octave, the other
the higher one. If we now start from the eighth note, considered as
the starting-point of a series similar to the first, and if we take care
to strike a new series of notes having between them the same

CHAP, vii.] MUSICAL SOUNDS. 187

degrees of pitch as the first, it will be noticed that the impression left
on the ear by their succession has the greatest analogy with that
which results from hearing the notes of the first scale. A melody
formed of a succession of notes taken from the first series, preserves
the same character if it is sung or played with the help of notes of
the same order taken in the second series. It would be the same
if we formed in a similar manner one or more gamuts higher or
lower.

A musical scale of this kind, formed of consecutive gamuts, is
unlimited, or at least has no other limits than those of our power
of perceiving sounds.

Before giving the intervals which separate the successive notes of
the gamut, or in other words the ratio of the number of vibra-
tions which correspond to each of them, we may remark that the note
from which we start to form a gamut, or to study music, is arbitrary,
as there are an infinite number of similar musical scales placed by
nature at the disposal of musicians. But, for the practice of music,
the want has been felt of taking conventionally a fixed point of
departure. Hence in modern music we find certain definite notes
(the vibrations of which are determined by the vibrations necessary
to produce one of them) called by certain definite names : the names
being the letters of the alphabet, A, B, C, T), E, F, G, repeated for
each octave. So long as it is merely a question of singing or of
music executed by the human voice, a convention of this kind is not
necessary, as the voice is an organ sufficiently flexible to emit at will
notes of any degree of acuteness or gravity within its natural limits.
Hence for such purposes we may consider the gamut as a thing
independent of any particular pitch, and it is convenient to call the
notes of such a gamut by some other names. Those used are derived
from the first syllable of each line of a Latin hymn written by

Faulus Diaconus :—

Ut quam laxis
7?esonare fibris
M ira gestorum
.Famuli tuorum
Solvi polluti
iabii reatum
SanctQ Johannes.

The Italians- substituted Do for Ut for the first note of the gamut, in
the seventeenth century.

188 PHYSICAL PHENOMENA. TBOOK TT.

Our arbitrary names for the seven notes of this gamut, which may
be independent of pitch, in passing from the gravest to the highest
note, are as follows : —

1st note. 2d. 3d. 4th. ftlh. 6th. 7th.

Do, Re, Mi, Fa, Sol, La, Si.

After what we have said of the manner in which the preceding
gamut is formed, and of the analogy, if not the identity, which exists
between the notes in different octaves, we can understand why the
same names have been given to the notes of the successive gamuts.
Musicians distinguish them by placing numerical signs after the
names of the notes, to mark the order of succession of the gamut.
The two scales we now give — one lower, the other higher than the
former — may for our purposes be written thus : —

Gamut above Do Ee Mi Fa Sol La Si

-i —i —i — i —i —i — i

Gamut below Do Re Mi Fa Sol La Si

2222222

It also results from the constitution of the successive scales that the
notes of the same name are an octave from each other, like the extreme
notes of each scale. Thus, Do— t, Ee— v Mi— t, are the acute octaves of
Do.2, Ee2, Mi2. Before proceeding further, let us recall the laws of the
vibrations of strings and tubes, and we shall understand that if we
stretch a series of seven strings, so as to make them give out the seven
notes of the scale, we shall obtain the seven notes of the acute scale,
the octave of the first, by dividing the strings into two equal parts. If
instead of strings we had taken seven open or closed tubes, giving the
scales by their fundamental notes, we must take seven tubes of half
the length to obtain the more acute scale, and seven tubes of double
the length to obtain the notes of the lower scale. If we compare, with
reference to their pitch, each of the seven notes of a scale to the lowest
note — to that which forms what is called the tonic, or key-note, there
are many different intervals, of which the names are as follows : —
From Do to Do Unison.

Re to Do Second.

Mi to Do Third.

Fa to Do Fourth.

Sol to Do Fifth.

La to Do Sixth.

Si to Do Seventh.

And lastly, Do to Du Octave.

—i

The musical interval is defined in physics as the relationship of
the numbers of vibrations of the notes of which it is formed. Unison

CHAP, vii.] MUSICAL SOUNDS. 180

and the octave are the only ones of which we have given the value :
1 or y measures the interval of unison ; 2 or f measures the octave.
It remains for us to speak of the numbers which measure the other
intervals. The following are those which are now adopted by the
majority of physicists : —

Do — Do Unison = 1

Re — „ Second = |

Mi - „ Third = £

Fa — „ Fourth = |

Sol—,, Fifth = f

La — „ Sixth = |

Si — „ Seventh = ^5

Do — „ Octave = 2

—i

As these only express the relationship, they can be written in the
form of whole numbers, and the seven notes of the scale will then be
found to be represented in one or the other of the following ways : —

Do Re Mi Fa Sol La Si Do

i I I i f f V 2

24 27 30 32 36 40 45 48

In other words, if the tonic or key-note, Do, be produced by 24
vibrations in a given time, the following notes will be produced by 27,
30, .... 48, &c.

It is easy to calculate by the aid of this table the consecutive
interval of the notes of the scale.

Do Re 'Mi Fa Sol La Si Do

«_ 101 0 .9. l_0 I) 1 <!

b i) l 5 a y 81 5

It will be seen that these intervals are not equal. The greatest,
although unequal, are called major seconds or tones, and the smallest
minor seconds or semitones. Although the major seconds are not
equal, it is agreed to place them under the same denomination, and
the scale is composed of the following successive intervals : —

A major second = tone.
A major second = tone.
A minor second = semitc
A major second = tone.
A major second = tone.
A major second = tone.
A minor second = semitone.

190 PHYSICAL PHENOMENA. [HOOK ji.

A scale thus formed is called the major scale, to distinguish it from
the scale formed of intervals succeeding each other in another order,
which is called a minor scale.

The musical scale thus formed is not sufficient for the composer
in the case of melodies, for if confined to such narrow limits they
would have a monotonous character incompatible with the variety of
impression he wishes to produce. To increase his resources, he
passes, in the same piece, from one scale to another ; and it is to
these transitions, the rules of which form so large a part of the art of
music, that the name of modulations has been given. The new scales
in which modulation is introduced differ only from the tonic scale in
the position of the new key-note ; the order of succession and the
relationship of pitch of the new scale remain the same. Let us write
the succession of two consecutive gamuts, from one octave to another : —
Do Re Mi Fa Sol La Si Do Re Mi Fa Sol La Si Do

We can readily comprehend how by a simple substitution of the
two intervals which separate the Mi from the Sol, — that is to say, by
causing Mi to be followed by a major second so as to precede the Sol
by a minor second, a fresh scale will be produced presenting the
same series of intervals as the first, but commencing by the note Sol
instead of by Do : as follows : —

Scale of Do Major.
Do Re Mi Fa Sol La Si Do Re Mi Fa Sol La Si Do

Scale of Sol Major.
Do Re Mi Fa Sol La Si Do

This may be written in ordinary musical fashion :

CD EF G A BC D EF G A BC

G ABC DE |FG

Hence by adding the sign J to Fa in the first scale, which means that
we lengthen the interval below it and reduce the interval to the next
note to a higher semitone, we have the two former octaves written
in the

Scale of Sol Major.
Do Re Mi FajfSol La Si Do Re Mi FajjSol La Si Do

Indeed it is seen that the two first intervals of this new scale are two
major seconds, Sol-La, La-Si, and that they are followed by a minor
second, Si-Do ; then follow three major seconds, Do-Be, Re- Mi, and Mi-

CHAP. VII.]

MUSICAL SOUNDS.

191

Fa$, so that at last the scale is terminated by a minor second, FaJ-Sol.
The new note must receive an entirely new name ; it is distinguished
from the Fa which it replaces by the name of Fa sharp : the Fa
natural is said to have been sharpened. But it is clear that we need
not regard these difficulties. We have only to consider the note Sol
as a new Do, and proceed as before modulated.

We can not only sharpen notes, as we have seen, but we can
flatten them ; this process is indicated by the sign b-

The following is the complete table of the major scales obtained

by this means : —

SCALE OF " Do " NATURAL MAJOR.

Sharps. Flats.

Scale of Sol 1 Scale of Fa 1

Re 2 Sib 2

La 3 Mib 3

Mi 4 Lab - 4

Si 5 Reb 5

Fa 6 Solb 6

Dojf 7 Dob 7

The series of notes sharpened successively is as follows : — Fa,
Do, Sol, Re, La, Mi, Si. The series of the flattened notes is precisely
inverse : — Si, Mi, La, Re, Sol, Do, Fa. The important point to re-
member is that these arrangements only alter the place of the start-
point ; the natural scale, when once the start-point is determined, is
invariable. As the complete exposition of the rules which serve to
form these musical scales would be beyond the range of this work,
we will restrict ourselves to saying that musicians also use minor
scales, presenting the peculiarity that the order of the ascending
intervals differs from that of the descending intervals.

MINOR SCALE.

Ascending intervals.

Descending intervals.

La2

. major second.

Soltf

. minor second.

. major second.

Latf

. major second.

. minor second.

Re '

. major second.

Fuji

. major second.

. minor second.

Soljf

. minor second.

. major second.

La0

192 PHYSICAL PHENOMENA. [BOOK u.

Iu this minor scale, we see that the two notes, Fa| and Solf of
the ascending scale are replaced by the two notes Fa, Sol, in the de-
scending one : musicians indicate this by using the symbol of each
of these two notes, the sign fc|, which they call a natural, and which
shows the return of the two sharpened notes to their primitive-
or natural state. The same sign also indicates a change of the same
kind in a note already flattened.

CHAP, vni.] OPTICAL STUDY OF SOUNDS. 193

CHAPTER VIII.

OPTICAL STUDY OF SOUNDS.

WE have described several different methods for counting the
number of vibrations executed by a sonorous body at the
moment when it gives out a certain sound : the toothed wheel syren
and vibroscope or phonautograph, are the instruments used for this
purpose. In the last, the vibrations themselves are inscribed on a
surface, and their amplitude and number can be easily shown : this is
the graphic method of the study of sound. M. Lissajous, a French
physicist, has during the last few years studied the vibratory move-
ments of sonorous bodies by the aid of the eye, and thus substituted
the organ of sight for the ear as a means of distinguishing the relation-
ship of sounds ; from this cause the method of examination is called
the optical method. The following is a brief description of it. By its
means even a deaf man might be trusted with researches on the rela-
tive pitch of sound. " There is no one among us," said M. Lissajous
in a lecture explaining the new method, " who has not, in his child-
hood, at the risk of setting fire to the paternal house, plunged a stick
into the fire, in order afterwards to move the glowing end with
rapidity through the air, to watch with the natural curiosity of youth
the brilliant lines of fire produced as by a magic brush, which appeared,
then vanished in an instant from the sight. This is the experiment
which forms the basis of the optical method."

194

PHYSICAL PHENOMENA.

[BOOK ii.

A tuning-fork is a little instrument formed of a double metallic
rod, the united branches of which form a long horseshoe, and are
supported by a cylindrical column resting on a stand (Fig. 1 34). By
inserting a piece of wood larger than the space between the two
extremities of the prongs, and rapidly withdrawing it, the elastic
prongs of steel are caused to vibrate, and their oscillations pro-

Pro. 134. — A tuning-fork mounted on a sounding-box.

duce a musical note, the pitch of which depends on the form and
dimensions of the instrument. Physicists sometimes produce vibra-
tions by drawing a bow across the prongs. The tuning-fork is used to
regulate the tone of instruments or voices in orchestras and theatres :
the normal tuning-fork is that which produces a certain definite
number of vibrations for the note C.

CHAP, vin.] OPTICAL STUDY OF SOUNDS. 195

To render the vibrations of a tuning-fork visible, M. Lissajous fixes
a small metallic mirror by its convex surface, at the extremity of one
of the prongs, while the other prong has a counterpoise to render the
vibratory movement regular.

" If we look in this mirror," he says, " at the images reflected from
a light a few yards distant, and then cause the tuning-fork to vibrate,
we observe that the image lengthens itself in the direction of the
length of the prongs. If the tuning-fork is then turned round on its
axis, the appearance changes, and we see in the mirror a bright
sinuous line, by the form of the undulations of which the greater
or less amplitude of the vibratory movement is indicated."

By using a second mirror, which reflects the image to a screen
after having passed through a convergent lens, the phenomenon can
be made visible to a large audience. In this case a brighter source
of light must be employed — that of the sun or the electric light,
for example — and the second mirror must be turned round a vertical
axis to obtain the transformation of the rectilinear image into a
sinuous curve.

Hitherto we have spoken solely of rendering visible the vibrations
of a single sonorous body. M. Lissajous has succeeded in distinguish-
ing the comparative pitch of two notes and measuring the relation-
ship of the numbers of vibrations which correspond to each of them.
Two tuning-forks are taken, both fitted with mirrors (Fig. 135) — but
whilst the axis of one is vertical, that of the other is horizontal — in
such a way as to have the two mirrors opposite to each other. A ray of
light issuing from a small orifice is thrown upon one of these mirrors :
it suffers reflexion, strikes the mirror of the second tuning-fork, and
is again sent back to a fixed mirror. A third reflection projects the
luminous ray on a white screen, where a clear and bright image of the
opening is visible so long as the two tuning-forks remain at rest.

If we cause the vertical fork to vibrate, we immediately perceive
that, instead of a point of light, the vibratory movement pro-
duces a luminous line, elongated in the vertical direction. If, while
the vertical tuning-fork is at rest, the horizontal one is caused to
vibrate, the image is elongated in a horizontal direction. Lastly, if
both forks are caused to vibrate simultaneously, the image which
results from the two movements, one at right^ angles to the other,
will describe a luminous curve on the screen, and the form of this

196

PHYSICAL PHENOMENA.

[BOOK ir.

curve will depend on the relationship which exists between the
durations of the two systems of vibrations, the amplitudes of the
oscillations, and lastly the time which separates the beginnings of
two consecutive vibrations executed by both forks. It is this time
which is called the difference of phase.

M. Lissajous has in this manner determined the luminous curves
given by forks tuned so as to produce the intervals of the scale, as
it is adopted by physicists.

FIG. 135. — Optical study of vibratory movements.

If the two tuning-forks are in unison, the relationship of the
number of vibrations is 1 ; in other words, the vibrations effected in
equal times are of equal number. The difference of phase is itself
nothing ; the vibrations begin at the same time in both tuning-forks :
there is a luminous oblique right line, the diagonal of a rectangle, the
sides of which have a length which varies with the amplitude of the
simultaneous vibrations. This right line is changed into an ellipse or
oval, when there is difference of phase. Fig. 136 shows the curves
given by differences of phase equal to J, J, f , and \. They are again
produced, but in an opposite direction, if the differences are f, }, |,
and 1.

When two forks are an octave apart they give a series of curves
represented in Fig. 137, which indicate that one of the forks executes

CHAP. VIII ]

OPTICAL STUDY OF SOUNDS.

197

a vibration in a horizontal direction, whilst the other
vertical direction.

FJO. 136.— Optical curves representing the rectangular vibrations of two tuning-forks in unison.

If the numbers of vibrations are in the ratio of 3 : 2, 4 : 3, 5 : 4,
5 : 3, 9 : 8, and 15 : 8, the forks are tuned to intervals of fifth, fourth,

FIG. 137.— Optical curves. The octave, fourth, and fifth.

third, sixth, major second, and seventh. In Fig. 137 the optical curves
obtained in the case of the fourth and fifth, with the variations of
form which proceed "from the differences of phase, are shown. By
studying these curves it is possible to count the number of vibra-
tions made by the luminous point in a horizontal and a vertical
direction ; and as they are all effected in the same time, we also

198 PHYSICAL PHENOMENA. [BOOK n.

learn the relative numerical relation of the two notes. When the
pitch of the forks agrees, the same curve continues on the screen
during the whole time of their simultaneous resonance, and it ends
by being reduced to a point. If, on the contrary, the pitch is not
quite the same ; if, for instance, the octave is not quite perfect, the
effect is the same as if there had been a continual changing in the
difference of phase, and the curve passes imperceptibly through
all the forms indicated in the figure. The time that it takes to
accomplish the entire round of these transformations being noted, it
is concluded that there is a difference of one vibration on the lowest
tuning-fork, and two vibrations on the highest, relatively to the
number which the true octave would produce.

This method is so precise that the slightest difference is detected.
Thus, let us suppose two tuning-forks in unison. The optical curve
will be one, according to the difference of phase, of those which is
represented by Fig. 136, and it will remain during all the vibrations.
If one prong of the tuning-fork is slightly warmed, it will cause a
decrease of pitch: the unison will be altered, and immediately we
observe a variation in the form of the optical curve produced on
the screen, which shows that the concord has ceased.

The optical method not only determines the relative numbers of
vibrations, but also shows the absolute number of the vibrations
which correspond to a given sound. Having once made a tuning-fork
which gives the normal concert-pitch of the note C, adopted by
orchestras, it is easy to use it afterwards as a type from which to
construct other tuning-forks in unison with it.

M. Lissajous has applied his method to the study of vibrating
strings, and even to that of sound propagated through air. In order
to effect this, he illuminates the string at one of its extremities, by
casting a luminous ray upon it. For the second purpose he receives
the movements of the air on a membrane to the surface of which
a small bright bead is affixed.

We have forgotten to mention that if, in all these experiments.
the curves traced by the luminous points are visible at the same
time in all their parts — that is to say, if an entire revolution is
terminated before the persistence of the impression of light on the
retina has ceased — as the duration of this persistence is about a tenth
of a second, we may infer that such is, at the maximum, the time

CHAP. VIII.]

OPTICAL STUDY OF SOUNDS.

199

employed by the image of the point in traversing the entire sinuosity
of the curve.

Such is the original method employed by M. Lissajous to render
vibratory movements, and the most delicate peculiarities of these
movements, perceptible to the eye. It will be seen, therefore, that we
were right in saying that a person deprived of the faculty of hearing
would be able to compare sounds with greater precision than the
most susceptible ear could do by hearing alone.

During the last few years a musician, M. Koenig, has invented
another very ingenious method of studying the
vibrations of columns of air in tubes, which we
shall now endeavour to describe. One of the walls
of a sonorous tube is perforated by a certain
number of openings — by three, for example, cor-
responding to the node of the fundamental note
and to the two nodes of its octave ; each of these
openings is closed by a small chamber from which
issues a gas jet communicating with a tube which
conveys the coal gas to the chamber and jet. That
part of the chamber which communicates with
the interior of the sonorous tube in contact with
the vibrating gaseous column is formed of a thin
sheet of caoutchouc, and is slightly extended by the
pressure of the gas. It is then eminently elastic,
and yields to the least increase of pressure. Let
us suppose the gas jet to be lighted : if the interior
pressure of air of the tube increases, the caout-
chouc membrane is compressed, so that the capa-
city of the small chamber diminishes and the flame
is elongated ; it shortens, however, if the pressure
diminishes, because the interior capacity of the
chamber then increases. It will be seen, therefore,
that the gas light is in reality a manometer, an
indicator of changes of pressure ; and M. Koenig
calls the flames which issue from the gas jets at the side of the pipe
manometric flames. Let us imagine that the sonorous tube is fitted to
a pair of bellows, and that the air inclosed by it is thrown into
vibration. We know that when a gaseous column vibrates, it is

Fio. 138. -Open tube with
manometric flame.

200 PHYSICAL PHENOMENA. [BOOK IT.

alternately condensed and dilated by the propagation of sonorous
waves. If the sound produced by the tube is the fundamental note,
the node is formed at the middle of the gaseous column : at this point
the dilatation and compression of the air attain their maximum. The
successive condensations and dilatations are then transmitted to the
manometric chamber of the middle portion of the tube, the flame of
which alternately elongates and shortens itself, executing a series of
movements which indicate the vibratory condition of the sonorous
body. If we cause the tube to give the octave of the fundamental
note, there will be a segment opposite to the middle chamber and
a node at each of the others. We shall then observe that the end
flames are very much agitated, whilst the middle flame will remain
immovable.

FIG. 139. — Manometvic flames. Fundamental note, and the octave above the fundamental note.

We know that in sonorous tubes the vibrating column of air is
divided into separate parts by the nodes, the middle points of which
are vibrating segments. At the nodes the air is at rest, but its density
is alternately at a maximum and minimum. On the other hand, each
vibrating segment is the point where the disturbance is at its greatest,
whilst the density of the air remains invariable. Now, as the varia-
tion of density determines the variations of pressure, and as these are
transmitted to the flames by the membranes of the chamber, it follows
that the manometric flames are very much agitated when they are
opposite the nodes, whilst they remain at rest if they correspond to a
segment of the vibrating column. M. Koenig's method enables us to
prove the existence of these different points : by reducing the flames to

CHAP. VIII.]

OPTICAL STUDY OF -SOUNDS.

201

a small size, the agitation which they undergo opposite the nodes puts
them out, whilst they remain alight opposite the segments. To make
the elongations and shortenings of the flame more sensible, M. Koenig
uses a mode of projection similar to that which M. Lissajous has
adopted for the optical method. He places a mirror near the jet of
gas, and causes it to rotate by means of toothed wheels and a handle.

FIG. 140. — Apparatus for the comparison of the vibratory movements of two sonorous tubes.

When the tube sounds, the revolving mirror shows a succession of
flames separated by dark intervals, or a luminous band with a toothed
edge. By placing a converging lens between the jet and the revolving
mirror, a clear and bright image is projected on the screen, where all
the peculiarities of the phenomenon can be studied.

202

PHYSICAL PHENOMENA.

[BOOK n.

Thus, in the two experiments which we have just described, where
the tube gives successively the fundamental note and its octave, the
change of light shows itself immediately in the manometric flames, as
shown by Fig. 139, where the upper series represents the effect pro-
duced by the vibration of the fundamental note, whilst the lower

FIG. 141. — Manometric flames simultaneously given by two tubes at the octave.

series proceeds from the note which is an octave higher. The number
of the flames is double in the second case.

The same result is obtained by fixing to a bellows two different
tubes, one an octave above the other, each of which is furnished

Fio. 142. —Manometric flames of two tubes of a third.

with a manometric chamber; when the flames are reflected on the
same revolving mirror, they give the two series which are represented
above (Fig. 141). To compare the pitch of the notes of tubes of
different intervals, M. Koenig employs another method. He causes
the gas, the combustion of which produces the flames employed, to
pass from one chamber to another, but only one jet is lighted. By
causing the two tubes to sound simultaneously, the same flame is

CHAP, viii.] OPTICAL STUDY OF SOUNDS. 203

agitated by the two systems of sonorous waves, and following each
other we see on the screen flames alternately larger and smaller, the
number of which depends on the musical interval of the notes.
" This disposition," says M. Koenig, " is even preferable to the first,
whenever the relation between the two tubes is not perfectly simple."
For example, for tubes giving C and E (a third) the observation of
four images corresponding to five becomes difficult ; but the suc-
cession of images which, by groups of five, are elongated and
shortened, and which are seen in the revolving mirror by the second
arrangement (Fig. 142), is not of a very complicated appearance.

B 2

204 PHYSICAL PHENOMENA. [BOOK n.

CHAPTEE IX.

QUALITY OF MUSICAL NOTES.

Simple and compound notes — Co-existences of harmonics with the fundamental
notes — The quality (clang-tint) of a note depends on the number of the harmonics
and their relative intensity ; M. Helmholtz's theory — Harmonic resonant
chambers (resonnzteurs) ; experimental study of the quality of musical notes
— Quality of vowels.

WE have seen that among the qualities of a musical note there is
one which distinguishes notes having the same pitch and
intensity. The A of a violin has not the same character as the A
of the flute or piano, or that of the human voice; and further, on
the same instrument a note does not sound the same if the mode
of producing it changes. Thus the note obtained by a violin string
vibrating its whole length is not identical with the same note
obtained from another string by the plucking with the finger.
Human voices can also be distinguished from each other, as we can
prove at any moment, although the notes may be of the same
intensity and pitch.

This particular quality of notes is called the quality, clang- tint,
or timbre.

For a long time very vague ideas prevailed as to the cause of this
singular modification of sound, and the hypotheses proposed by several
mathematicians — among them Euler — could never be verified by expe-
riments. In the present day, thanks to the labours of a contemporary
German philosopher, M. Helmholtz, this obscure part of the science
of acoustics has been fully explained: and the cause of the quality
of sound has been discovered. Some very ingenious instruments
constructed by M. Koenig have considerably simplified the experi-
mental verification.

CHAP, ix.] QUALITY OF MUSICAL NOTEa 205

When a string, tube, rod, or any sonorous body produces a note,
we have, besides the fundamental note, the pitch of which can be
easily distinguished by the ear, more feeble notes, which correspond
to vibrations of less amplitude and variable velocities, effected by
different parts of the sonorous body. The co-existence of these
vibrations produces a compound note; on the one hand, the most
intense fundamental note ; and on the other, harmonic sounds whose
numbers of vibrations are multiples of the number of vibrations
of the fundamental note.

According to M. Helmholtz, the clang-tint of a note depends at
once on the number of harmonic notes which accompany it, and on
the relative intensity of each of them. The exactitude of this
explanation has been proved by the following means: —

A series of hollow copper globes of different sizes, pierced with
two openings of unequal diameter, were constructed in such a manner
that in each of them the interior
mass of air resounds when a body
giving a certain note is placed before
the large opening (Fig. 143). These
are called resonance globes, and their
property consists in strengthening
the notes for which they are tuned,
and by which the air which they
inclose is thrown into vibration.
This being established, M. Koenig

Constructed an apparatus formed Of FIG. 143.— M. Helmholtz's resonance globe.

eight globes tuned to the series of

the harmonic sounds, 1, 2, 3, 4, 5, 6, &c. : for example, for the notes do2,
do3, sol3, do±, mi4, sol^ &c. Fig. 144 shows them fixed on a stand one
below the other ; they each communicate by an india-rubber tube
placed over the small opening with a manometric chamber ; the gas
jets of these chambers are placed parallel to the revolving mirror, and
by the agitation or repose of these flames, we can easily see on the
surface of this mirror which of the globes has entered into vibration.
When a sonorous body, a tuning-fork, for instance, is caused to vibrate,
and is moved before the openings of the globes, the note is strengthened
as soon as it passes before that which gives out the note of the same
pitch ; and the flame of this globe appears agitated in the mirror. If

20C

PHYSICAL PHENOMENA.

[BOOK ii.

then, a compound tone is produced, to study the harmonics of this
note and their relative intensity, the sonorous body must be moved
bofore the openings of the globe, and certain flames will be seen
agitated whilst the others remain at rest. As the agitation is faster
or slower, the intensity can be calculated.

By this means we can show that a variation in the clang-tint of
a note of certain pitch results from the difference of the harmonics
which compose it, and from the predominance of one or other of
its secondary tones.

FIG. 144 — M. Koeuig's apparatus for analysing clang-tints.

M. Helmholtz, by applying this method to the study of the clang-
tints of vowels, has discovered that the vowel A, for example, is pro-
duced by a compound of certain harmonics ; so that when the larynx
emits this particular sound, the mouth is in such a position as to give
the predominance to such of the harmonic notes as are required.

CHAP, ix.] QUALITY OF MUSICAL NOTES. 207

The harmonics vary for each vowel sound, and are produced by the
cavity of the mouth, &c., being so arranged as to resound most
strongly to the harmonic required. Thus in the case of the vowel-
sound 0, we require the fundamental and a strong higher octave;
A requires the third ; E an intense fourth ; while in U the harmonics
are thrown into the shade.1

1 This interesting subject is treated at some length in Professor Tyndall's work
on " Sound," to which we refer for further particulars.

208 PHYSICAL PHENOMENA. [BOOK n.

CHAPTER X.

HEARING AND THE VOICE.

ALL physical phenomena are revealed to man by the impressions
which they produce on his organs. To him they are simple or
compound sensations, according as one or several senses conduce to
their production. Thus it is by the help of the organ of sight that
we see light; by touch that we perceive the sensation of heat; the
efforts our muscles make to lift a heavy body, the sight of a falling
stone, reveal to us the existence of gravity ; and the ear gives us the
sensation of sound.

But to study the phenomena in themselves, and to discover the
conditions and the laws of their production, it is necessary for us to
distinguish in the sensations experienced what belongs to our organs,
and what is a stranger and external to them : by this means only the
real nature of the phenomena becomes intelligible to us. In truth,
this abstraction is never complete, because there cannot be one
observation or one experiment which does not require the presence of
man and the intervention of one or other of his senses to prove the
results. How shall we, then, succeed in abstracting ourselves, so to
speak, in the study of physical phenomena ? It is by varying in all
possible ways their modes of production, as well as the methods which
we use to observe them ; in a word, it is by the mutual control of the
sensations, one over the other, that the truth can by degrees be brought
to light, and the phenomena appear to us in their individuality and

CHAP, x.] HEARING AND THE VOICE. 209

independence. Thanks to the use of these methods, we now
know the nature of sound ; we know that it consists of a peculiar
movement of the molecules of elastic, solid, liquid, or gaseous elastic
bodies. We have already proved the existence of sonorous vibra-
tions and studied their laws. It remains for us to know how these
vibrations are communicated to our organs, until the time when
they form, so to speak, an integral part of our being, when the
disturbance which they communicate to our nerves is transformed
into a particular sensation, which is the sensation of sound. The
ear is the special apparatus in man and all animals, designed to
collect sonorous vibrations and to transmit them to the auditory nerve.
Let us endeavour to explain what, according to the anatomists, is
the disposition and role of the different parts of this organ.

Every one knows the external ear, situated on each side of the head,
and composed of two parts, — the ala, or wing, and the auditory canal.

The ala or wing of the external ear (concha), A (Fig. 145), consists
of a cartilaginous membrane, its form varying with different persons.
Generally it is of an irregular oval shape, becoming smaller at
its lower part. At the centre there is a sort of funnel, the trumpet
which forms the entrance of the auditory meatus, B, a kind of tube
or sonorous pipe which terminates at a certain point where the
intermediate ear begins : there, separated from the auditory canal by
a very thin and delicate membrane, c — the tympanic membrane — is
the tympanum, a sort of drum (D), known as the drum of the ear. The
membrane of the tympanum is inclined very obliquely to the axis
of the auditory nerve, so that its surface is much greater than the
cross section of the canal at the point of its insertion. The drum
of the ear is pierced with four openings, two of which are through
the wall which faces the membrane, and as one is of a circular and the
other of an elliptical form, they are designated the round and the oval
window ; the latter the fenestra ovalis of our anatomists. At the
lower part of the tympanum enters by the third opening a canal, I,
which makes communication between the middle ear and the outer
air through the intervention of the nasal fosses. Lastly, a fourth
opening is in the upper part of the drum. In the interior of the
tympanum there is a series of little bones known as the chain of
small bones, or auditory ossicles. Fig. 146 represents the forms and
relative positions of these. One, the hammer (malleus), M, rests on

210 PHYSICAL PHENOMENA. [BOOK n.

oue side on the membrane of the tympanum, and the other on the
anvil, E (incus). The two others are the lenticular bone, L (os orbicu-
lare), and the stirrup (stapes), K, both named on account of their
form. The bottom of the stirrup is joined to the membrane which
is tightly stretched over the fenestra ovalis. Two little muscles help
to move the hammer and the stirrup, to support them with more
or less force against the adjoining membranes, and to prevent too
violent motion.

Behind the drum of the tympanum is the internal ear, which
appears to be the most essential part of the organ of hearing. It is

FIG. 145. — The human ear ; section of the interior tympanum ; chain of small bones.
Internal ear ; labyrinth.

protected by the hardest parts of the temporal bone which anatomists
call the petrous bone. Three separate cavities compose the internal
ear : they are, the vestibule, at the middle ; the semicircular canals, G,
at the upper part ; and the cochlea, H, at the lower part. The whole
forms the labyrinth, the interior of which is covered with a membrane
which bathes in a gelatinous liquid, the perHym/ph* Into this liquid
plunge the ramifications of the auditory nerve, which penetrates to
the labyrinth by a bony canal called the inner auditory meatus.

Such is a description of the principal parts which constitute the
organ of hearing in man : as we descend the animal series, the

CHAP, x.] HEARING AND THE VOICE. 211

external and middle ears gradually disappear, but in proportion as
the organ is simplified the remaining parts are more developed. It
only remains for us to explain the use of each of them.

Evidently the object of the external ear is to collect and reflect
sonorous waves into the opening of the external auditory canal. This
is proved by the fact that animals which have the wing of the ear
movable turn this opening towards the place whence the sound
comes, as soon as their attention is awakened. Man has not this
faculty ; but it has been observed that the most delicate ears belong
to those whose ear-wing is furthest from the skull ; and we all know
that to be able to hear better, it suffices to enlarge the surface
artificially with the hollow of the hand. The external auditory
canal transmits the sonorous vibrations, after strengthening them,
to the membrane of the tympanum, then by the chain of small
bones to the inner ear.1 The Eustachian tube, by bringing the outer

FIG. 146. —Details of the auditory ossicles. FIG. 147.— Section of the cochlea.

air into the box of the tympanum, maintains on both sides of the
membrane the same pressure.

As to the small bones, besides their function of transmitting vibra-
tions to the inner ear more easily and energetically than a gaseous
body would do, it appears certain that they transmit the motions
from the tympanic membrane to the fenestra ovalis, and perhaps
that they stretch the membrane of the tympanum and that of the
fenestra, ovalis, and thus render them more susceptible to vibratory
movement. Hence the difference which exists, as regards sensa-
tions between the nodes of hearing which are characterized by the

1 The solid parts of the head and the teeth directly transmit sonorous vibrations
to the internal ear. If we suspend a bell to a string between the teeth, and stop
the ears, a deep sound is transmitted by the thread, the teeth, and petrous bones to
the internal ear. Deaf people, whose infirmity is only owing to a bad conformation
of the internal organs, can hear in this way.

212

PHYSICAL PHENOMENA.

[BOOK ii.

two words to listen and to hear. The person who only hears does
not undergo such a strong sensation, because the action of the will
is not interfered with. On the other hand, as soon as he listens
he instinctively gives the order to the muscles of the hammer and
of the anvil to act; the membranes are stretched, and the sound
becomes more intense and distinct. This idea, proposed by Bichat,
is adopted by physiologists and philosophers. It appears that the
degree of tension of the membrane of the tympanum also varies
with the degree of acuteness or depth of the sound to be heard;
to perceive acute sounds, the membrane is stretched much more
than if they were deep sounds. In Professor Huxley's " Lessons on
Elementary Physiology," it is stated that the membranous labyrinth
distinguishes intensity and quantity of sound ; while the finer qualities
are discriminated in the cochlea, the scala media of which represents
a key-board of a piano, the fibres of Corti the keys, and the ends of
the nerves the strings. There is therefore a fibre ready to take up
any particular note of vibration, and it is deaf to all others.

We have said above that the inner ear is the most essential part of
the organ of hearing ; and, indeed, it has been proved that the membrane
of the tympanum and the small bones can be lost without deafness
ensuing, always providing that the two windows of the tympanum are
not torn, for then the liquids which moisten the auditory nerve flow

away, the organs of the inner
ear, as well as the ramifica-
tions of the nerve itself, be-
come dried up, and- they lose
their sensibility. In this case,
there is absolute deafness.

From the preceding re-
marks we see that the theory
of hearing still presents some
difficulties ; but ifc is rather
the task of physiologists than
of physicists to dissipate them

entirely. That which is so admirable in this organization of one of
the most useful senses for the conservation of the individual, and
his relations with his fellows and the outer world, and which is the
source of the most delicate and profound enjoyments, is the wonderful

FIG. 148. — Auditory apparatus of fishes ; ear of the Ray

CHAP. X.]

HEARING AND THE VOICE.

213

faculty to hear an indefinite number of sounds. The co-existence
of vibrations in the air and in media suitable for the propagation
of sound accounts for this property of the ear, which transmits to
the nerves and thence to the brain the thousand modifications of
the elastic medium among which we live.

Let us conclude this study of the phenomena of sound by a short
description of the organ of the voice in man, that natural musical
instrument by the aid of which we communicate our ideas in their

Fio. 149. — The human voice ; interior view of the larynx. Glottis ; vocal chords.

most delicate and intimate shades, an instrument so flexible and com-
plete that the most perfect artificial contrivance cannot imitate it in
the diversity of shades and qualities which enables the human voice
to express the most varied sentiments and passions.

The -vocal organ is nothing more than a wind instrument ; that is,
the sounds are produced by more or less rapid vibrations of the air, in

214 PHYSICAL PHENOMENA. [BOOK IT.

its passage through an opening of particular form more or less re-
stricted. The air passes from the lungs by a tube or annular canal, N,
called the windpipe ; from that it penetrates into the larynx, M, where
it enters into vibration and produces the notes of the voice, then
into the pharynx, a funnel which enters the back of the mouth.
The sound then arrives in the cavities of the nasal fosses and of
the mouth, which acts as a resonant chamber and gives a special
clang-tint to the note.

Fig. 149 shows the interior conformation of the larynx. It is as
it were a kind of cartilaginous box, the base of which terminates hi
the windpipe, N, and the summit by the hyoid bone, formed like a
horse-shoe. The epiglottis, E, is a sort of movable valve, which by
descending can close the larynx at its upper part, thus preventing
food from penetrating into it, which would produce extinction of the
voice, and suffocation. Underneath the epiglottis is the glottis, K,
an opening comprised between two systems of folds leaving a cavity
between them called the ventricles of the larynx. These folds
bounding the glottis are the so-called "vocal chords," or ligaments:
these are elastic cushions, with broad bases and sharp, free, parallel
edges ; they are stretched to a degree of tightness which enables
them to vibrate quickly so as to produce audible sounds, the vibration
being set up by the passage of the air. When quiescent, the glottis
is V-shaped, and air can pass without producing sound.

Physiological experiments have shown that the vocal chords vibrate
like the serrated mouths of sonorous tubes, and that sounds thus pro-
duced are more or less acute according as the tension, more or less
strong, of the vocal chords modifies the form and dimensions of the
opening between them called the glottis. When the note arrives in
the mouth, its pitch is determined ; it is not submitted to any other
modifications than those which constitute the clang-tint, or which
form the articulated voice. The movements of the pharynx, tongue,
and lips serve to produce these various changes, which we have not
the space to speak of here. We will only state that men's voices,
differing from those of women or children by their depth, owe their
character to the greater dimensions of the larynx and the opening
of the glottis. The rapid development of this organ in young-
people, towards the age of puberty, is the cause of the transforma-
tion which we observe in their voices.

BOOK III.

LIGHT.

BOOK III.
LIGHT.

WE are about to enter a fairy-like, enchanted world, a world of
wonders, where rubies, sapphires, topazes, and all kinds of
precious stones send forth their fires ; where every object is of in-
comparable beauty and splendour ; in a word, into the world of
light and colour.

Thus, the cycle of the phenomena of nature gradually passes in
review before us. After having studied the physical forces, more
particularly in their mechanical action, this action being so general
and so constant that it appears to give us more the idea of matter, we
have now to notice a series of phenomena more variable and more
directly connected with the movements of organized beings, the prin-
ciple of which is a condition of life — the phenomena of light and heat.

It is difficult if not impossible to have a clear idea of the nature of
the phenomena of light on the surface of the various celestial bodies
which people space. But, on the earth, what variety and magnificence
we witness during the day and the night ! If the eye of man cannot
look at the dazzling star when it shines in all its brilliancy in a cloud-
less sky — if even the portion of the sky surrounding the solar disc
hurts the sight — the whole country, on the other hand, is resplendent,
and sends us back the rays which inundate it. Moreover, thanks to
this double journey of the rays of light, from the sun to the terrestrial
objects and from them to us, a wonderful transformation is effected.
The source of all this emits but one tone, one colour, while a multi-
tude of shades and various colours are sent back to us by the objects
seen. This metamorphosis is so familiar that we do not even suspect
it : each body appears to us to possess in itself a colour of its own, and
the presence of a luminous source, whatever it may be, at first appears
to have no other influence than to render it perceptible.

218 PHYSICAL PHENOMENA. [BOOK in.

The variable nature of atmospheric conditions also adds to the
beauty of the spectacle by the continual changes which it brings in
the thousand shades of light and colour. During the night the spectacle
is different: it is a softer light which slowly succeeds the diurnal
illumination : but the charm thus becomes even more grateful. The
light of the moon in its different phases, the millions of stellar fires
which sprinkle the dark azure of the starry vault, the misty veil
with which the landscape is enveloped, multiply, with the gli aimer of
twilight and the aurora, the various beauties of the scene. Light and
colours ! . . . . For the artist there is such a powerful magic in these
words, that often, being smitten with passion for them alone, he sees
nought else, and considers them as alone the objects of art. But lie
has no need to visit museums to enjoy these beautiful things: the
Eembrandts, Lorrains, and Veronese have drawn their inspiration from
the country. Eich jewel-cases do riot help us to admire the wonders
of light. He who knows how to observe can. without even changing
his place, see them displayed around him : a ray of sunlight which
penetrates into his room and passes through a glass of water, the
morning or evening horizon, dewdrops which shine suspended like
diamonds or pearls on the leaves of trees, the rainbow colours of
a liquid bubble, and a thousand other phenomena which are con-
tinually following and modifying each other, — surely this is an
inexhaustible source of pictures for an artist, a subject full of
studies for the man of science.

Light gives us all this : day and night, dazzling illumination and
feeble glimmers which traverse the profound darkness, decided colours
and innumerable shades, oppositions and transitions, similitudes and
contrasts, and always harmony. Is it then astonishing that primitive
races, in their simple ignorance, reserve their adorations, through
admiration and gratitude, for the Source whence came both light and
heat ? This was in their minds" the beneficent and fruitful Sovereign,
the true God of the universe. Modern science, less respectful but
more intelligent, placed face to face with physical agents, has tried to
solve the secrets of the phenomena of light, and has succeeded, with
the help of a delicate and profound analysis, in discovering the
principal laws. The result of these beautiful researches will now be
the object of our exposition.

Let us first consider the principal sources of light.

CHAP, i.] SOURCES OF LIGHT ON THE EARTH. 219

CHAPTER I.

SOURCES OF LIGHT ON THE SURFACE OF THE EARTH.

Sources of cosmical light : the sun, planets, and stars —Terrestrial, natural, and
artificial luminous sources — Lightning ; Polar aurorse ; electric light ; volcanic
fires ; light obtained by combustion.

T IGHT sources may be divided into two classes, according to their
-L^ origin : the first, the cosmical, are exterior to the earth ; the second
exist on our planet or in its atmospheric envelope. The Sun must
be placed first among the cosmical sources of light. - It is the most
powerful source of all to us. The mean brightness of its light is,
according to Wollaston, 800,000 times greater than that of the full
Moon ; and as the brightest star in the sky, Sirius, does not give much
more than the 7,000th part of the Moon's light, it follows that it
would require at least five thousand six hundred millions of similar
stars to illuminate the earth to an equal extent to that of the Sun.
It is well known that the movements of rotation and translation of
our planet are of such a nature that the light of the Sun is periodically
distributed over each part of its surface. The light is variable
according to the season and hour of the day, the greater or less
elevation of the solar disc above the horizon having much to do
with its apparent luminous intensity ; but the interposition of the
vaporous masses which constitute clouds, mists, and fogs, tends also
considerably to enfeeble it.

The solar light reaches us some time after the Sun has sunk below
the horizon. The upper strata of the air remain directly illuminated
when the Sun has ceased to light up the place of observation and the
lower strata ; and this is the cause of twilight, the length of which is
prolonged by a phenomenon which we shall soon study under the
name of " refraction of light."

s 2

220 PHYSICAL PHENOMENA. [BOOK in.

Among those lights which are of celestial origin, there are some
which are not direct luminous sources : the Moon, for example, which
makes our nights so bright, receives her light from the Sun before
reflecting it to us. This is also the case with planets and their
satellites.

The sources of light which have their origin on our planet may be
divided into natural and artificial. The lightning in storms, fire
produced by volcanic eruption, polar aurorae, so frequent in northern
and southern regions, together with shooting stars and bolides, and
perhaps the zodiacal light must be ranked with the former. We may
also add those lights which are developed in certain organized beings,
the phosphorescence of certain insects, the marine infusoria known
as the Noctilucce, some being vegetable and some mineral.

We all know that light can be procured artificially by combustion,
which is nothing more than chemical combination accompanied by the
disengagement of light and heat. Electricity is also a source of light ;
and science, as we shall presently learn, has succeeded in utilizing its
powerful light, the intensity of which is so great that it can only be
compared to the dazzling brightness of the Sun itself.

CHAP, ir.] LIGHT IN HOMOGENEOUS MEDIA. 221

CHAPTER II.

THE PROPAGATION OF LIGHT IN HOiMOGENEOUS MEDIA.

T IGHT is propagated either in vacuo, or within certain solid, liquid,
J-^ or gaseous media. When we speak of vacuum, we mean not
the absolute vacuum of philosophers, but a space entirely deprived of
all tangible substance, as the interplanetary space probably is, or the
space above the mercury in a barometer, and in vessels exhausted
by an air-pump. The fact that light reaches us from the Sun and
stars, and passes through the exhausted receiver of our laboratory,
proves that light, unlike sound, does not require a ponderable medium
for its propagation. As regards the passage of light through the air
and different gases, through water and a great many other liquids, and
lastly, through solids like glass, special experiments are not required
to prove this.

We also know that luminous bodies are not the only ones which
produce in us the sensation of light; but they serve to light others
and to render them visible. Bodies thus illuminated then become
secondary luminous sources, whence light emanates, to be propagated,
through the media of which we have just spoken, as direct light.
Bodies may, then, be arranged, as regaids their property to emit,
receive, or allow light to pass through them, into different classes :
viz., self-luminous, non-luminous transparent, and non-luminous
opaque bodies.

222 PHYSICAL PHENOMENA. [BOOK in.

Transparency and opacity are never absolute. Light which passes
through bodies like air, water, or glass, is always pactly absorbed ;
and observation proves that absorption is greater in proportion to
the thickness of the substance traversed by the light. Objects
may be clearly seen through a plate of glass or a shallow layer of
water ; but in proportion as the thickness increases, the clearness
decreases : the colourless medium, which at first appeared to be inter-
posed between the eye and the objects, begins to assume a deeper tint,
until the light is totally absorbed, and at last nothing is seen but the
medium itself. A white disc was plunged into the sea off the coast
of Civita Yeoohia when the water was perfectly clear, of a beautiful
colour, and of great purity, and it was found entirely to disappear at a
depth of 50 yards (experiments of M. Cialdi). " At first the disc
became slightly greenish, then a clear blue, and this blue darkened in
proportion as the apparatus was allowed to descend, until the colour,
having then become as dark as that of the water, could not be dis-
tinguished from the surrounding medium/' Discs of a yellow or mud
colour disappeared under the same circumstances at depths of from
17 to 24 metres.

The transparency of gases, and of atmospheric air when it is pure,
is much greater. From a very considerable elevation like that of Mont
Blanc, the eye enjoys a grand panorama, and can distinguish objects
at a considerable distance. According to M. Martins, the portion of
the earth's surface geometrically visible from the top of Mont Blanc
has a radius of 130 miles. It would therefore be possible, if the air
were absolutely transparent, to perceive the Gulf of Genoa; but
" beyond 60 miles the objects are obscured by a haze, and
become confusedly seen, or effaced. For a distance of 35 miles
everything is clear and recognisable." Luminous points would
without doubt be seen during the night at the limits of the range of
visibility : such was the opinion of M. Martins and the scientific men
who accompanied him, since they proposed to exchange fire signals
with the town of Dijon, one of the points of this immense horizon.

In addition to transparent or diaphanous substances, there are some
which are simply translucent, through which light is able to pass, with-
out permitting the colours or the shape of objects to be distinguished
through them : ground glass, paper, horn, alabaster, and certain liquids,
such as milk, are examples. By wetting paper, or by covering it with

CHAP, ii.] LIGHT IN HOMOGENEOUS MEDIA. 223

a thin layer of oil, its translucency is increased, and may even be
changed into transparency if the paper is sufficiently thin.

Even substances which are believed to be absolutely opaque allow a
certain quantity of light to pass through them when they are cut into
very thin plates. Stones, wood, metal, and many other substances are
opaque. Nevertheless, if we place between the eye and a luminous
source a sheet of gold leaf, for instance — gold-beaters obtain it so thin
that 250,000 put together have not the thickness of an inch — we
see a beautiful green colour, which proves the transmission of light,
not through holes produced during the beating, but through the very
substance of the metal itself. The extreme smallness of the objects of
which microscopists examine the internal structure — infusoria, micro-
phytes, &c. — doubtless explains their transparency.

When the light emitted by a luminous source or an illuminated
body reaches the eye, it can only do so by passing through diaphanous
or translucent media. Let us inquire what is the course of its pro-
pagation, and what effect is produced if it meets in its path with
bodies of greater or less opacity ? Such are the simplest problems
of which philosophers have demanded a solution by experiment in
studying these phenomena.

The most simple case is that in which light traverses a perfectly
transparent homogeneous medium ; one, that is, of the same density
and composition throughout ; and reaches the eye in a direct manner.
Experiment proves that it is propagated in a right line. Between the
flame of a candle and the eye, let us interpose a series of opaque
screens, each pierced with a little hole : in order to see the light, it is
obvious that the holes of all the screens must be in a straight line.
Daylight cannot be seen through a long tube if this tube is not recti-
linear, or at least if its curvature is too great to allow a straight line
to pass through it without touching the sides. Shut yourself in a per-
fectly close and dark room, and admit the light of the sun by a little
hole made in the shutter. Almo&t immediately you will see a lumi-
nous cone which marks the passage of the light through the air, and
you will easily prove that the outlines of this cone are perfectly
rectilinear. In this case, it is not the air itself that we see, but
the particles of dust suspended in the air made visible by illumina-
tion on the dark ground of the room.

The propagation of light in a straight line can also be proved when

224

PHYSICAL PHENOMENA.

[BOOK in.

the sun, hidden by an accumulation of clouds, emits its rays "between
their openings. We then see projected into the atmosphere, long rays

FIG. 150. — Propagation of light in a straight line.

more or less luminous, which visibly proceed in a right line. But we
shall presently see that as the atmosphere is composed of strata of

FIG. 151. — Rectilinear propagation of light.

variable densities, the light which successively passes through these
strata no longer moves in a straight line. On the surface even of the

CHAP, ii.] LIGHT IN HOMOGENEOUS MEDIA. 225

earth, in order that this movement be exactly in a straight line, the
transparent medium must be perfectly homogeneous, whether this
medium be air, or gas, water, glass, &c.

Let us now explain what scientific men mean by the terms ray,
beam, and pencil of rays.

Light emanates or radiates from luminous bodies in every
direction ; and is propagated in a straight line, as we have just seen, in
homogeneous media. A luminous 'ray is a series of points regarded
simultaneously or successively, of which one of the lines followed by
the light is composed ; a pencil is a collection of small rays starting
from the same source, and a beam or bundle of rays is the union
of many parallel rays. Luminous pencils are cones having their

FIG. 152.— Cone of shadow of an opaque body. Completed shadow.

summits at the source of light. But when the luminous source is very
distant, as in the case of the sun and stars, the rays coming from the
same point of the source have such a slight divergence that they
may be considered parallel, and we have a beam.

If there were in nature nothing but self-luminous bodies and
media of absolute transparency, we should only see the former. Not
only is the transparency of the various media imperfect, but a
multitude of bodies interfere with the passage of light, scatter it in
all directions, and become illuminated, or, in other words, visible.
From this fact result half-tones and shadows.

226

PHYSICAL PHENOMENA.

[BOOK in.

When an opaque spherical body is in the presence of a luminous
point and at a certain distance from it, one part of the body, that
towards the light, is illuminated, the other does not receive light.
It is in shadow. Moreover those portions of space situated beyond
the dark surface of the body receive no light, as we can easily prove
by placing a screen behind the body and observing the shadow thrown
on the screen. The luminous point is, in this case, the summit of a
cone tangent to the outlines of the opaque body, a luminous cone
in its fore part and dark in its prolongation, which is called the cone
of shadow. In this case, which is never perfectly realized, the portion
of the opaque body not illuminated is totally invisible (Fig. 152), and
the separating line of the shadow and the light is exactly marked.

When the source of light is a luminous body of finite dimensions,
the case is otherwise. Fig. 153 clearly shows that the surface of a

FIG. 153. — Cones of umbra and penumbra

body lighted up is divided into three parts : one ot whicn is lighted
up at the same time by the whole of the luminous surface ; another
which receives no light • and a third, intermediate between the others
which receives only a fraction of the total light, and which constitutes
what is called the penumbra. The space situated behind the opaque
body, opposite the luminous source, is likewise divided into an absolute
cone of shadow, and a cone enveloping the body which is the cone of
the penumbra. Beyond this double cone, the space is entirely illumi-
nated. If the luminous body is greater than the opaque one, the cone
of shadow is limited ; it is cylindrical, if the two bodies are equal ; and

CHAP. II.]

LIGHT IN HOMOGENEOUS MEDIA.

227

lastly, we see a divergent cone if the opaque body is larger than the
illuminating one (Fig. 153).

The penumbra gives to the outlines of illuminated round bodies
that half-tint which renders the contrast between lights and shades
softer and less decided. As the cone of the penumbra continues to widen
more and more, it follows that the full shadows cast by an illuminated
opaque body are paler and less clear, as its distance from the screen is

FIG. 154. — Silhouettes or perforated cards ; effect of the umbra and penumbra.

greater. Every one can prove this for himself. The perforated cards
which are given as playthings to children are an application of the
effect of the half-light produced by penumbras. When the card
is very near the wall or screen on which the shadow is thrown, this
shadow is well denned, and the effect which the artist desired to pro-
duce is not obtained ; at a proper distance, the penumbra, spread out

228

PHYSICAL PHENOMENA.

[BOOK in.

to a greater extent, produces the desired effect (Fig. 154) ; but if
this distance is too great, the image becomes confused.

The propagation of light in a straight line explains the phenomena
observed in a dark room. Shut yourself up in a room, the window of
which is completely closed, a very small hole being made in a thin
part of the shutter, and let it be by this hole alone that the rays of
a luminous body — the sun, for instance — are able to penetrate into
the room. Then place a white screen at a certain distance from
the opening, you will see a luminous spot of circular or elliptical
form, which becomes larger as the distance from the screen to the
opening is increased (Fig. 150). It is the image of the sun.

If instead of the solar light we permit that of a candle to enter the
dark room, we see reproduced on the screen the image of the candle

FIG. 155. — Inverted image of a candle.

and its flame, inverted. The reason of this inversion is very simple.
The rays which leave the upper extremity of the flame pass through
the hole, continue their passage in a right line in the dark room, and
paint a luminous point at the lower part of the screen. Those which
proceed, on the other hand, from the base of the flame, form their
image at a higher point. The image therefore is naturally reversed,

CHAP. II.]

LIGHT IN HOMOGENEOUS MEDIA.

229

and this explains both why this image exists, and why it is seen
upside down. A card pierced by means of a needle gives the reversed
image of a candle as shown in Fig. 155.

The form of the opening is also immaterial : round, square, or
triangular, it always gives the image of the light-source with its
exact form. Let us suppose the opening to be of triangular form ; and
allow the rays of the sun to penetrate it, receiving them on a screen

FIG. 156.— Images of the Suu through openings in foliage.

placed normally to their direction. Each point of the disc will give
a pencil of light which, penetrating through the hole, will mark out
on the screen a section of like form to the opening, that is, triangular.
All these elements will be superposed ; and as there is no part of
the shape of the disc which is not given, it follows that the form
of the image will be circular, like that of the sun.

230

PHYSICAL PHENOMENA.

[BOOK in.

This explains why, in the shadow projected by a tree, the light
which penetrates the interstices between the leaves always has a
circular or elliptical form, according as the rays fall on the ground
perpendicularly or obliquely (Fig. 156). During eclipses of the sun,
it has been observed that these images of the luminary take the form
of a luminous crescent, much more curved than the solar disc itself.

If the shutter of the dark room is opposite a landscape illuminated
by the sun, or even by the diffused light given by a clear sky, each

FIG. 157. — Dark chamber. Reversed image of a landscape.

object will paint its reversed image on the screen, and a faithful
reproduction of the landscape will be seen (Fig. 157). If the screen is
perfectly white, all the colours and their shades will be admirably
reproduced ; but the image will be clearer in proportion as the
opening is smaller and the landscape more distant.

By saying that light is propagated, we admit implicitly that it
is not transmitted instantaneously from one object to another; that
it takes a certain time to traverse the distance which separates the
luminous object from the eye which it enters, or from the object
which it illuminates. This truth had been suspected for some time

CHAP. IL] LIGHT IN HOMOGENEOUS MEDIA. 231

by philosophers and men of science, but the demonstration was only
furnished about two centuries ago. The velocity of light is so great
that it appeared at first infinite, at least for distances which could
be measured on the surface of the earth. In one second, light passes
through a space of not less than 300,000 kilometres, or 180,000 miles.
It does not take more than a second to come from the moon (approxi-
mately) ; but it takes 8 minutes 13 seconds to come from the sun : a
very rapid voyage, nevertheless, when we bear in mind that a cannon-
ball would take nearly twelve years to accomplish it, supposing that
it preserved a uniform velocity of 540 yards per second. Again, the
velocity of light is 900,000 times greater than that of sound through
air at 0° C., and it moves 10,000 times faster than our planet in
its orbit.

How, then, have physicists succeeded in measuring such a rapid
movement ? We will endeavour to explain.

Let us imagine that a flash of light — for example, the ignition
of a heap of gunpowder — is produced periodically at perfectly equal
intervals of time, say every ten minutes. Whatever may be the
distance of the observer from the spot where the phenomenon
takes place, it is evident that, from the first explosion, all the others
will appear to succeed each other at successive intervals of ten
minutes, whether the velocity of light be small, considerable, or
infinite, provided that the observer remains at a fixed distance from
the point where the explosion occurs.

But if, at the instant of the first explosion, the observer begins
to move further away, he will, obviously, perceive a delay at each of
the following explosions, a delay which will go on increasing and will
be due to the time that the light takes to traverse the increase of
distance ; for instance, at the twelfth explosion, if he is 20 kilometres
further off and the delay notic'ed is two seconds, must he not conclude
that light travels 10 kilometres per second ? The same inference may
be drawn from an analogous experiment ; if, for example, instead of
a luminous flash, it was the periodical disappearance of a light
which was observed.

Now a phenomenon of the latter kind takes place in the heavens.
The planet Jupiter is accompanied in its movement of translation
round the sun by four satellites which revolve round it in regular
periods. The planes in which the movements of these little bodies take

PHYSICAL PHENOMENA.

K III.

place coincide, very nearly, with the plane of Jupiter's orbit. Now,
Jupiter, being opaque, projects behind it, that is to say, in the direction
from the sun, a cone of shadow, the axis of which is in the plane of its
orbit. It therefore follows that, in their successive revolutions round

FIG. 158.— Measure of the velocity of light by the eclipses of Jupiter's satellites.

the central planet, the satellites traverse this cone at the period of
their opposition. During the time of their passage through the
shadow, the light which these bodies receive from the sun is inter-

CHAP, ii.] LIGHT IN HOMOGENEOUS MEDIA. 233

cepted ; in a word, they are eclipsed. The eclipses of Jupiter's
satellites are very frequent, especially of those which are nearest the
planet ; and, from the earth, it is easy to observe their emersions and
immersions by using a telescope of medium power. When the satel-
lite drawn by its movement of revolution round the plant has just
penetrated the cone of shadow, its light is extinguished: this is
the immersion. It continues its course in the shadow until the
moment when, coming out of the cone, its light reappears : this is
the emersion. These two phenomena are not visible from the earth
during the same eclipse, in the case of the two satellites nearest to
Jupiter, because these satellites are hidden by the opaque body of the
planet, sometimes at the moment of their immersion and sometimes
at that of their emersion. Moreover, they cannot be observed in
any way at the period of conjunction or opposition, the cone of
shadow being entirely hidden by the disc of the planet, as is easily
explained by Fig. 158. It is also easy to see why the immersions
are visible to us from the period of conjunction to the following
opposition, whilst the emersions, on the contrary, are visible from
opposition to conjunction.

Jupiter moves in the same direction as the earth, but much more
slowly in his orbit. When the earth is at T and Jupiter is at J on the
prolongation of the radius vector T s, this is the period of conjunction.
From this instant, the earth describing a certain arc on its orbit, and
Jupiter an arc of less amplitude on his, the observer finds himself
carried to the right of Jupiter's cone of shadow, and from that time
he can see the immersions of the satellites. The same circumstances
take place until the time when, the earth being at T', Jupiter is at j',
also on the prolongation of the radius, but away from the sun ; that
is to say, until the opposition. Then, by the fact of the simultaneous
movements of the earth and Jupiter, the first of these planets is car-
ried to the left of the cone of shade projected by the second, and the
emersions of the satellites are visible until the new conjunction T", j".

These preliminaries being understood, we can easily explain how
astronomers are able to deduce the velocity of light from observation
of the eclipses of which we have just spoken.

Let us take, for instance, the first satellite of Jupiter, that is to say,
the one nearest the planet. Its movement of revolution is known with
such precision that it is possible to calculate the intervals of its

234 PHYSICAL PHENOMENA. [BOOK in.

eclipses with the greatest accuracy, or rather the intervals which
separate either two consecutive immersions or two emersions. Now,
observation proves that the duration of these intervals is not con-
stant ; that they appear to be shortened in proportion as the earth gets
nearer to Jupiter, and on the other hand to be increased as it passes
further away, whilst they are perceptibly equal at the two periods
when the distance from the earth to Jupiter varies but little, that is to
say, at conjunction and opposition. If then we calculate the period
of a future immersion according to the mean duration of the intervals
separating two successive immersions, and compare the result of
the calculation with that given by observation, it will be found that
the phenomenon appears to be delayed when the earth is distant from
Jupiter, and to advance, on the contrary, when it is near to it. More-
over, the delay or advance is always in exact proportion to the
increase or decrease in the distance between the two planets.

It is no longer doubtful that the difference between the result
of calculation and observation is really due to the time which the
light takes to traverse the unequal distances which we have just
mentioned. From conjunction to opposition, or from opposition to
conjunction, it has been found that the successive accumulations of
these differences produce a total advance or delay of about 16 minutes
30 seconds. Now, the distances T j, T" j", exceed the distance T' j' by
an amount of space which is precisely the diameter of the terrestrial
orbit. It requires, then, 16 minutes 30 seconds for light to travel
across this interval, or, in other words, 8 minutes 15 seconds for the
half, which is the distance from the Sun to the Earth ; nearly equal
to 146,000,000, kilometres (91,000,000 miles).

This gives, as we have before said, a velocity of 300,000 kilo-
metres, or of 186,000 miles per second.

The discovery of the velocity of light by the eclipses of Jupiter's
satellites is due to Eoemer, a Danish astronomer, who explained it in
a memoir presented to the Academic des Sciences in 1675. Since
the time of Eoemer, the discovery of aberration by Bradley at once
confirmed both the moment of translation of the earth, and the suc-
cessive propagation of light in space. We see that the exactness of
the number which measures the velocity of light depends here on the
knowledge of the sun's distance. The same thing happens when this
velocity is deduced from aberration. But in the first case, it is the

CHAP, ii.] LIGHT IN HOMOGENEOUS MEDIA. 235

velocity in the vacuum of celestial space ; whilst in the second case,
it is that of light passing through the air. The two methods have
given nearly the same results.

Lastly, during the last few years, two physicists, MM. Fizeau and
Foucault, have succeeded in directly measuring the velocity of light
by purely physical means. The following are the main points of
the method devised by M. Fizeau.

By means of an instrument represented in Fig. 159 he sent a pencil
of luminous rays from a lamp, from Suresnes — where he was stationed
— to Montmartre, where a mirror was placed, reflecting the light back
again exactly to the point of departure. The light of the lamp at first

FIG. 159. — M. Fizeau's instrument or the direct measure of the velocity of light.

fell, after having traversed a system of two lenses, on a mirror, M,
formed of a piece of unsilvered glass, inclined at 45° in the direction
of the luminous rays. From this it was reflected at a right angle,
and, after its passage through the object-glass of a telescope which
made the rays of light parallel, it passed across the distance which
separated the two stations. Having arrived at Montmartre, the
parallel bundle of rays traversed the second object-glass and con-
centrated itself on a mirror which sent it back, following the same
route, to the first inclined mirror. There the reflected pencil, passing
through the unsilvered glass, could be examined by the observer
by means of an eye-piece. By this arrangement M. Fizeau was
able to observe at Suresnes the image of the light placed near him,

236 PHYSICAL PHENOMENA. [BOOK in.

after the rays had made the double journey which separates Suresiies
from Montmartre.

The question was, to determine the time which light took to
traverse this distance. In order to ascertain this, M. Fizeau placed
in the path of the rays a little in front of the mirror M and at the
point where the rays, which emanated from the lamp, were brought to
focus, the teeth of a wheel K, to which a clock-work mechanism gave
a very rapid and uniform movement.

Every time that the movement of the wheel brought a tooth in the
path of the pencil of light, this tooth served as a screen, the light was
intercepted ; whilst it freely passed through the space which separated
one tooth from another. It was exactly as if a screen were alternately

FIG. 160.— Measure of the velocity of light by M. Fizeau.

1. The luminous point seen through the teeth of the fixed wheel.

2. Partial eclipse of the luminous point.

3. Total eclipse.

placed before and removed from the path of the light. Let us suppose
that, at the commencement of rotation, the wheel, at present at
rest, presented one of its openings to the passage of the light : the
image reflected from the luminous point is seen clearly by the
observer. If now the wheel is turned, but with such a velocity that
each tooth requires to take the place of the space which precedes it a
longer time than that required by the Hght to go to Montmartre and
return to Suresiies, — what will happen ? The luminous ray at its
return will obviously again find free passage through the very space
which it traversed at the moment of departure ; the luminous point will
be visible; but, in proportion as the velocity of rotation increases, the
intensity of the light will diminish, because of all the luminous rays
which pass through each of the intervals, there is an increasing number

CHAP. IT.] LIGHT IN HOMOGENEOUS MEDIA. 237

which, on their return, will find the passage closed. If, at last, the
velocity of the wheel is such that the time taken by one tooth to take
the place of the space which precedes it, is precisely equal to that
which the light takes to traverse the double distance between the two
stations, there is not a single luminous ray passing through the wheel
at leaving, which does not, on its return, find the passage closed;
there will be a continual eclipse of the luminous point, as long as
the velocity of which we speak remains the same.

This is sufficient for the purpose, because an index fitted to the wheel
indicates the number of revolutions which it makes per second ; and
the number of teeth and of spaces is known : the time which a tooth
requires to take the place of a space is then known, and it will be
seen that it is exactly equal to that which the Jight takes to travel
twice the 8,633 metres which separate the two stations. M. Fizeau
thus found that light travelled 196,000 miles (315,000 kilometres)
a second ; a result agreeing with that furnished by the observation
of Jupiter's satellites when the distance of the sun deduced from
the ancient parallax of that body is adopted.

Some time after M. Fizeau's experiment, in May and June 1850,
some instruments, based on the principle of rotating mirrors adopted
by Mr. Wheatstone in measuring the velocity of electricity, have
enabled it to be shown that light moves with greater rapidity through
air than through water, so that the relations of the two velocities have
been determined. MM. Leon Foucault and Fizeau have each succeeded
in attaining the same result. Lastly, in 1862, the first of these experi-
menters, modifying his first apparatus, went still further ; he succeeded
in measuring the time which light takes to travel the little distance
of 20 metres, a time which is equal to the hundred and fifty millionth
part of a second. According to later experiments of M. Foucault,
the velocity of light through space is 298,000 kilometres a second,
a little less than that obtained by M. Fizeau, but which agrees with
that deduced from observations of the eclipses of Jupiter's satellites,
adopting the new parallax of the sun.

238 PHYSICAL PHENOMENA. [BOOK m.

CHAPTEE III.

PHOTOMETRY. — MEASURING THE INTENSITY OF LIGHT SOURCES.

Luminous intensity of light sources, illuminating power — Principles of photometry
— Law of distances — Law of cosines — Rumford's photometer — Bouguer's
photometer — Determination of the illuminating power of the Sun and the full
Moon — Stellar photometer.

WE all know, by everyday experiment, that the illuminating
power of a light varies according to the distance at which
the object illuminated is placed from the source of light. When we
read in the evening by lamp or candlelight, we can also observe that,
without changing the distance we are from the light, it is possible,
by inclining the pages of our book in a certain way, to obtain various
degrees of illumination. Lastly, if instead of one light we place
many at the same distance, or, again, if instead of a small lamp we
substitute a very large one with a wide wick, it will be evident to us
that the illumination will be augmented in a certain proportion.

The illuminating power also varies with the nature of the lumi-
nous source, other things being equal. The flame of a gas-jet appears
to us much more brilliant than that which is given by an oil lamp ;
the light of the moon is infinitely less bright than that of the
sun, although the discs of the two bodies have nearly the same
apparent size.

When the intensity of the source of light is sought for, certain
circumstances must be taken into account; some being inherent in
the light sources themselves, others peculiar to the object illuminated,
such as distance, inclination, &c. The problems relative to determi-
nations of this nature constitute the branch of optics called pho-
tometry, from two Greek words which signify — the first, light; the
second, to measure.

CHAP, in.] PHOTOMETRY. 239

Nothing is more delicate or difficult than the measurement of lumi-
nous intensities. In spite of all progress realized in the science of
optics, there are yet no instruments which give this measure with an
exactness comparable to other physical processes. The harometer
and thermometer respectively give us with extreme sensibility the
pressure of the atmosphere and the temperature ; the relative pitch of
two sounds can be distinguished with great delicacy. Photometry is
in a less advanced condition, and the comparison of the intensity of
two lights leaves much to be desired. This arises from the fact that
we have no other criterion in this case than the organ by the aid of
which we perceive the lights to be compared. The sensation of sight
is the only judge, and, in spite of its extreme sensibility, the eye
is but slightly fitted to determine the numerical relations of two or
more lights which are before it either simultaneously or successively.

Even when it has to judge of the equality of two light sources,
the difficulty is great. If the observations are not simultaneous, the
comparison will be the more difficult according to the interval of
time which elapses between them. We must first arrange, therefore, —
and that is not always possible, — that the two lights be observed
together.1

Very frequently the brightness of the sources of light dazzles the
eye, and renders it incapable of judging with the least precision ;
and this is the reason why physicists, instead of comparing the
sources of light themselves, observe similar surfaces illuminated by
these sources under similar conditions of inclination and distance.
Again, the diversity of the colours of lights is a cause of uncertainty

1 " In this manner the judgment of the eye is as little to be depended on as a
measure of light, as that of the hand would be for the weight of a body casually
presented. This uncertainty, too, is increased by the nature of the organ itself,
which is in a continual state of fluctuation ; the opening of the pupil, which admits
the light, being continually expanding and contracting by the stimulus of the light
itself, and the sensibility of the nerves which feel the impression varying at every
instant. Let any one call to mind the blinding and overpowering effect of a flash of
lightning in a dark night compared with the sensation an equally vivid flash pro-
duces in full daylight. In the one case the eye is painfully affected, and the violent
agitation into which the nerves of the retina are thrown, is sensible for many seconds
afterwards in a series of imaginary alternations of light and darkness. By day no
such effect is produced, and we trace the course of the flash and the zigzags of its
motion with perfect distinctness and tranquillity, and without any of those ideas of
overpowering intensity which previous and total darkness attach to it." — SIR JOHN
HERSCHEL.

240 PHYSICAL PHENOMENA. [BOCK in.

which cannot be obviated. " Between two differently coloured
lights," says Sir J. Herschel, " no parallel susceptible of precision
can be drawn ; and the uncertainty of our judgment is greater as
this difference of coloration is more considerable."

In spite of .these difficulties there have been established, either
by reasoning or by experiment, a certain number of principles which
have suggested the invention of various photometrical intruments,
some of which we will now describe. In the present day, when
public and private gas-lighting has become very general, and the
want has been felt of facilitating navigation on our coasts by
establishing numerous lighthouses, photometers have become instru-
ments of which the practical utility is equal to the interest of the
purely scientific problems for which they have been invented. But
it is not less certain that the first processes invented for the com-
parison of the sources of light are due to men who by no means
thought of the question of practical utility. In the seventeenth
century Auzout and Huyghens, in the following century Andre Cel-
sius, Bouguer, and Wollaston, kept in view the interesting, although
purely speculative, question of the relative brightness of the light
of stars. They endeavoured to determine the intensity of the sun's
light compared with that of the moon or the brightest stars.

The first principle which they enunciated was the following : —
When the distance from a' luminous point to the object illuminated
varies, the intensity of the light received varies in the inverse
ratio of the square of the distance. And, indeed, the light radiates
from the luminous point in every direction with equal force;
but these rays diverge as the distance increases. If they are
received on the surface of a sphere of a definite radius, they will
produce on one element m of this sphere an illumination of a
determinate intensity; if, continuing their path, they are received
upon a sphere of double radius, the same rays which are spread on
the surface m will be on the surface M of the new sphere. Now,
geometry teaches us that M possesses four times the surface of m,
and, inasmuch as the same quantity of light is spread over a surface
four times greater, it may be concluded that its intensity is four
times less. At triple the distance, the intensity is nine times less :
in a word, the intensity of light diminishes as the square of the
distance increases. This has been confirmed by experiment as we

CHAP, in.] PHOTOMETRY. 241

shall presently see. This law holds good only if we abstract the
absorption of luminous rays by the media in which they move. It is
also applied to the case in wtuch the source of light is no longer a
simple luminous point, but presents an apparent appreciable surface,
provided that it be distant enough from the illuminated object to
allow the latter to le regarded as equidistant from all parts of the
source. It follows from this first principle of photometry, that if we
present to the light of a candle, for instance, a piece of white paper,
and remove it further and further away to distances 2, 3, 4 times

FIG. 161. — Law of the square of distances.

greater, the brightness will become nearly 4, 9, 16 times less. It is
necessary that the paper be always placed perpendicularly to the
direction of the luminous rays.

If, without changing the distance, the paper is inclined in one
direction, it is evident that the brightness will diminish, since the
same surface will now intercept a less number of rays. The quantity
of light received then varies according to a law which is called the
law of cosines, because it is proportional to the cosines of the angles
which the luminous rays make with the perpendicular to the illumi-
nated surface.

The foregoing remarks refer only to the illuminating power of the
source of light, not to its intrinsic brightness. If this intrinsic bright-
ness does not vary, it is clear that the illuminating power will be
greater as the surface of the source itself is greater ; so also in the
case where the intrinsic brightness is increased, the illuminating
power is increased in the same proportion.

242 PHYSICAL PHENOMENA. [BOOK HI.

Oue inference from the preceding principles is, that a light source
possesses the same apparent intrinsic brightness, whatever may be
its distance from the eye ; for, although the quantity of light which
penetrates the opening of the pupil diminishes in the inverse ratio
of the square of the distance, still, as it emanates from a luminous
surface, the apparent diameter of which appears smaller and smaller,
and which decreases in the direct ratio of the square of this same
distance, there is exact compensation, and the brightness of the
source remains the same at each point. This is why the light of
the planets, such as Venus, Mars, and Jupiter, appears to us always
equally bright when we see them at the same height above the
horizon, if the purity of the atmosphere is the same, although their
distances from the earth are variable. The sun is seen from the
different planets as a disc, the apparent surface of which varies from
about 1 to 7,000 : the quantity of light that each of these bodies
receives varies in the same proportion ; but the intrinsic brightness of
the disc is the same at Mercury as at Neptune ; if we suppose that
the celestial spaces do not absorb light, and that it is subjected
to the same degree of extinction in its passage through the atmo-
spheres of the two planets.

We all know that if we look at a red-hot ball in the dark, the
spherical form is no longer perceptible to the eye, and it appears like
a flat disc, every portion of which shows the same luminous intensity.
If, instead of a spherical ball, a prismatic bar of iron or polished
silver is brought to incandescence, an analogous phenomenon will
present iteelf. Whatever may be the position of the bar, its edges
will not be visible, the brightness will be the same everywhere, on
the sides presented perpendicularly to the eye as on those which are
more cr less inclined; in a word, the observer will believe that he
is looking at an entirely plane surface. Let the bar be caused to
revolve, and the movement will only be noticed by the apparent
variation of width of the luminous band. The conclusion to be
derived from these experiments is, that the quantity of light emitted
by a solid incandescent body in a definite direction depends on the
inclination of its surface to the direction of the luminous rays.
Indeed, if two units of surface, one on the side of the metallic bar
which fronts the observer's eye, the other on an inclined side, should
emit in that direction the same quantity of light, it is quite evident

CHAP. III.]

PHOTOMETRY.

243

that the inclined side would appear to have the greatest brightness,
since the same number of rays would be spread over an area the
apparent size of which is less. The sun is a luminous sphere ; but
its aspect is that of a disc, the intrinsic brightness of which is not
greater at the border than at the centre,1 which confirms the law we
have just announced, which is called the law of the cosines, because
the quantity of light emitted by equal surface areas of a light source
varies as the cosines of the angles which the rays make with a
normal to the surface. These are the principles upon which the
measurement either of the illuminating power or the intrinsic
brightness of sources of light depend.

We will now describe the instruments called photometers, which
are used to measure these intensities. Rumford's photometer is repre-

FIQ. H>2. — Rumford's photometer.

sented in Fig. 162. It is based on the fact, that if shadows thrown
on the same screen by an opaque body illuminated by two different
lights have the same intensity, the illuminating powers of the
two lights are equal, if they are at the same distance from the

1 It is now proved that the central parts of the solar disc are the most luminous,
contrary to what would be the case if there were an equal emission of light over the
whole surface. Astronomers, however, have shown that this appearance is due to
an absorbing atmosphere of small height, so that more light is absorbed at the
borders than at the centre.

U 2

244

PHYSICAL PHENOMENA.

[BOOK in.

screen, or are in the inverse ratio of the squares of these distances,
if they are at unequal distances. Let us suppose that we wish to
compare the illuminating powers of a jet of gas and an ordinary
candle. A black cylindrical rod is placed vertically in front of a
screen of white paper, and the two lights are arranged so that the
shadows of the rod will both be projected on the paper, nearly in
contact. Then we gradually move the light which gives the most
intense shadow, until the eye can no longer distinguish any difference
between the intensities of the shadows. To judge better of the
equality of the shadows, we look at the screen on the side which
is not directly illuminated by the candle and the flame of the gas.
At this moment, the luminous parts of the screen receive the rays
of both lights at once, whilst each shadow is only lighted by one
of them : the equality of their tints then indicates the equality of
the illuminating powers of each separate source. The illuminating
powers of the two lights are then, according to the first principle, in
the inverse ratio of the squares of their distances from the screen.

Fio. 163.— Bouguer's photometer.

Bouguer's photometer (represented in Fig. 163) is based on the
equality of brightness of two portions of a surface separately illumi-
nated by each of the light sources.

An opaque screen prevents the light of each source from reaching
that part of the surface which is illustrated by the other. This
surface formerly consisted of a piece of oiled paper, or ground glass.

CHAP, in.] PHOTOMETRY. 245

M. Leon Foucault uses in preference a plate of very homogeneous
porcelain, sufficiently thin to be translucent. The two illuminated
portions are separated by a narrow' line of shadow projected through
the screen, and the eye placed behind judges easily of the moment
when the illumination is equal. This equality once obtained, the
intensities, of the lights are deduced from their respective distances
from the plate of porcelain. We will confine ourselves to the
description of these two kinds of photometers, both of which serve
to prove the law of the square of distances. Tho verification is very
simple : it is sufficient to put on the one side one candle : it will
then be found that there must be placed four at double the distance,
nine at triple the distance, to obtain either equally dark shadows
on the screen, or equal illumination in both portions of the sheet of
porcelain. The following are some of the results obtained by the
instruments : —

If we use two equal lights, two candles, for instance, and if we
place one of them at a distance eight times further from the screen
than the other, it will be found that the shadow of the first dis-
appears. At this distance the intensity of its light is sixty-four
times less than the other. Bouguer, to whom we owe this experi-
ment, concluded that one light, of whatever intensity, is not per-
ceptible to our eyes in presence of a light sixty-four times brighter.
This explains to us how it is that, in broad daylight and in a clear
sky, the stars are no longer visible ; why from the interior of a well-
lighted room we see nothing but darkness out of the windows, and
again, why we can scarcely distinguish, when in full sunlight, what
passes in the interior of an apartment.

Bouguer and Wollaston both tried to compare the light of the
sun with that of the full moon, taking as comparison the light of
a candle. They both found that the sun's light was equal to the
united light of about 5,600 candles placed at a distance of 30
centimetres. As to the light of the full moon, Wollaston found it
equal to the 144th part of that of a candle placed at the distance of
3in>65. Whence he concluded, by easy calculation, that the light of
the sun was equal to about 800,000 times that of the full moon.
Bouguer only found the number 300,000. Quoting the number
obtained by Wollaston, a number which differs much from that of
the French philosopher, Arago adds : " I cannot tell in what consists

246 PHYSICAL PHENOMENA. [BOOK in.

the enormity of this number compared with Bouguer's determination,
for the method employed was exact, and the observer of incontestable
ability."

It will be seen from this how difficult photometrical determina-
tions are, especially when they refer to lights, the intensity of which
is as prodigiously different as those of the sun and moon. Much has
yet to be done in devising new experimental methods.

CHAP, iv.] REFLECTION OF LIGHT. 247

CHAPTEE IV.

REFLECTION OF LIGHT.

Phenomena of reflection of light — Light reflected by mirrors ; diffused light ; why
we see things — Path of incident and reflected rays ; laws of reflection— Images
in plane mirrors — Multiple images between two parallel or inclined surfaces ;
kaleidoscope — Polemoscope ; magic lantern — Spherical curved mirrors ; foci
and images in concave and convex mirrors — Caustics by reflection — Conical
and cylindrical mirrors — Luminous spectres.

LONG before human industry, stimulated by the requirements of
luxury and frivolity, had dreamed of polishing metals and
glass in order to make their surfaces brilliant for mirrors and looking-
glasses, nature presented many examples of the phenomena which
physicists call the reflection of light: for the surface of limpid and
tranquil water, as of a pool or lake, reflects a faithful image of the
country which surrounds it, the azure vault of the sky, clouds, sun>
stars, trees, rocks, and the living beings who walk on the banks and
sail over the liquid surface. This is on a large scale the model
which industrial art has to copy, and which would enable us to study,
not only conveniently but accurately, the path which light takes
when, coming from luminous sources or illuminated objects, it is
reflected from the surface of bodies. The necessity of comprehending
never precedes that of admiring and enjoying, and the discovery of
the laws which govern the reflection of light was doubtless made long
after the imitation of the phenomena we have just described.

Light is not always reflected in the same manner from the surface
of bodies. The reflection varies according to many circumstances,
among which we shall first consider the nature of the reflecting
substance and the condition of its surface.

If we consider bodies whose surface is naturally smooth and
polished, like liquids in a state of rest, mercury, &c., or susceptible of

248 PHYSICAL PHENOMENA. [BOOK in.

acquiring this quality by mechanical processes, as glass and most
of the metals, &c., the reflection of light from their surface will not
show these bodies themselves, but the illuminated or luminous
objects which are situated in front of them. Light reflected in this
manner produces the images of these objects, the dimensions and
form of which depend on those of the reflecting surface ; but in pro-
portion as the degree of polish is more perfect, the light and colour
will be better preserved. These are reflectors or mirrors. Physicists
then say that light is reflected regularly or specularly.1

When light is reflected by bodies possessing a tarnished, dull, or
rough surface, it does not produce images, but it shows the bodies from
which it emanates, so that each point of their illuminated surface
serves for other objects the part of a luminous point. The light
which a polished surface receives is never entirely reflected. If the
body is transparent or translucent, a portion of the received light
penetrates into the interior and traverses the substance, and is usually
partly extinguished or absorbed. It is often a very small amount of
the luminous rays which are reflected from the surface.

If the body is opaque, the reverse takes place ; the light received
is in great part reflected, bat a certain quantity is absorbed by the
thin strata at the surface of the body.

Let us next consider the path which light follows in the pheno-
menon of reflection, always supposing the medium homogeneous.
Very simple experiments, which every one can verify more or
less rigorously, will indicate to us the laws which govern this
propagation. Let us employ a bath of mercury for a reflecting
surface, and for a luminous object a star, the rays of which, coming
to the surface of the earth from a distance which is practically
infinite, may be considered exactly parallel. The direction of the rays
coming from the star and falling on a certain point of the mirror
formed by the mercury is easily determined by means of a theodolite,
the axis of which is fixed in an exactly vertical position (Fig. 165).
If we look directly at the star, the line i' s' of the telescope indicates
the direction of the incident luminous rays, and the angle s' i' N',
equal to the angle s I N, is the angle of incidence; that is to say, that
formed by a luminous ray with the perpendicular to the surface at
the point of incidence.

1 From speculum, a mirror.

Fio 164. -Phenomena of reflection.

CHAP. IV.]

REFLECTION OF LIGHT.

251

In order to find the direction of the reflected luminous rays, we
must turn the telescope on its axis until we see the image of the star
on the surface of the mercury bath. When the image is brought to
the centre of the telescope, it is certain that the angle R' i' N' is equal
to the angle of reflection NIK. Thus, in reading the measure on the
graduated circle of the instrument, the angle of reflection can be com-
pared with the angle of incidence. Now, whatever may be the star

FIG. 165. — Experimental study of the laws of the reflection of light.

observed, and whatever its height above the horizon, it is always
found that there is perfect equality between these angles. Moreover,
that position of the circle of the theodolite which enables the star
and its image to be seen evidently proves that the ray which arrives
directly from the luminous point, and that which is reflected at the
surface of the mercury, are in the same vertical plane.

252 PHYSICAL PHENOMENA. [BOOK in.

These two laws have been expressed by physicists in the follow-
ing form : —

The angle of incidence is equal to the angle of reflection.

The incident and the reflected ray are loth in the same plane, which
is perpendicular to the reflecting surface.

These are two very simple laws, but they suffice to afford an expla-
nation of the most complex phenomena, and of the action of the most
varied optical instruments, whenever these phenomena and instru-
ments have reference to the reflection of light from the surface of
bodies. We shall soon be able to judge for ourselves.

In the first place we will speak of the images which appear on
the surface of mirrors, that is to say, of all bodies sufficiently polished
to allow the light which falls on their surfaces to be reflected in a

FIG. 166. — Reflection from the plane mirror. Form and position of the images.

regular manner. These images vary in dimensions and form with the
form and dimensions of the reflecting surface ; but it will be sufficient
for us to give some idea of the luminous effects produced by plane,
spherical, cylindrical, and conical mirrors.

We all know that mirrors with a plane surface — such as looking-
glasses and liquid surfaces in a state of rest — show images which
faithfully represent the objects which they reflect. The dimensions,
form, and colour are reproduced with exactitude ; the image alone is
always symmetrical with the object, so that the right side of one is
the left of the other, and vice versd. Again, the apparent distance of
the image behind the mirror is precisely equal to the real distance
of the object in front of the mirror. Fig. 166 perfectly explains
these conditions.

CHAP, iv.]

REFLECTION OF LIGHT.

253

All the luminous rays which the extremity of the flame of a
candle throws upon a plane mirror, diverge in every direction after
their reflection from the surface of the mirror ; but the equality
of the angles of incidence and reflection causes these rays to con-
verge behind the mirror at a point symmetrically situated in rela-
tion to the luminous rays. The eye which receives one of these
rays will then be affected as if the luminous object were situated
at the point of convergence, and it will there see the image. What-
ever may be the position of the observer in front of the mirror, the
position of the image will be the same, although it appears to occupy
different points on the same
mirror. The lower end of the
candle will form its image
in the same manner, and
so with all the intermediate
points. From this it is seen
that the image of any lumi-
nous object will be formed,
point by point, of all the
partial images symmetrically
situated behind the mirror,
at distances from its surface
equal to the distances of each
of the points of the object.

Fig. 167 shows how the
image of an object can be

Seen in a plane mirror, With-
, . -, t • , t • 1 • T

out the object being directly
in front of it; it suffices that the eye be placed so as to receive
the reflected rays, that is to say rays in the divergent space Q M M' P.
This is called the field of the mirror.

In mirrors, or ordinary looking-glasses, the form and colour of the
reflected objects are generally slightly altered, because it is difficult to
obtain a perfect polish and an exactly plane surface. The diffused
light is then mixed with the light reflected from the mirror, and
communicates to it the colour which the substance of the mirror
possesses. We also observe in tinned mirrors that the objects
frequently form a double image : one, the more feeble of the

FIG. 1«7. -Reflection from a plane mirror.
Field of the mirror.

254 PHYSICAL PHENOMENA. [BOOK in.

two, is formed on the exterior surface of the mirror; the other,
the more brilliant, is that which is given by. the mirror properly
so called, that is to say, by the internal tinned surface. Metallic
mirrors have not this inconvenience, but they possess others
which are much greater : the quantity of light that they reflect is
not so great, and their surface tarnishes rapidly in contact with
the air.

If we place two or more plane mirrors in various ways, we obtain
singular effects from the multiple reflections which are cast back
from one mirror to another.

FIG. 168. — Reflections from two plane parallel mirrors. Multiple images.

The most simple of these effects is that which is produced by
two plane parallel mirrors (Fig. ll)8). A luminous object interposed
between the two mirrors shows on each of them one image, av oly
which becoming a luminous object to both mirrors, gives rise to two
new images more distant than the first, a2, o2. These form new ones,
and so indefinitely ; so that with the eye conveniently placed, we
shall see an infinity of images which become more arid more feeble
on account of the loss which the light undergoes by each successive
reflection. These effects are easily observed in a room containing
two parallel and opposite looking-glasses. The two series of images
soon become confused when they are influenced by a luminous point?

CHAP, iv.]

REFLECTION OF LIGHT.

255

but if we wish to distinguish them it is sufficient to look at an
object the surfaces of which are of different colours and forms.

Two plane mirrors forming an angle produce images the number
of which is limited and dependent on the angle. But they are all

Fio. Itj9. — Images on two mirrors inclined at right angles to each other.

observed to be placed in a circle, having for its centre the point of
intersection of the mirrors, and for its radius the distance from the

FIG. 170. — Images in mirrors at right angles (DO").

FIG. 171. — Images in mirrors at 60°.

luminous point. Figures 170 to 172 represent the images formed
by mirrors inclined at 90°, 60°, and 45°. The first system gives
three images, the second five, and the third seven. These multiple

256

PHYSICAL PHENOMENA.

[BOOK in.

reflections have suggested the construction of various instruments,

among which may be mentioned the kaleidoscope, invented by

Brewster.

In a pasteboard tube are fixed three plates of glass forming an

equilateral prism, the bases of which are closed respectively by two

parallel plates, one of transparent,
the other of ground glass, between
which are placed little objects, such
as pieces of coloured glass. The
eye, on looking through the smaller
end of this kind of telescope, sees
these pieces of glass, the multiple
images of which are formed by
reflection on the three mirrors ;
hence result regularly disposed
figures, which can be varied at
FIG. i72.-images in mirrors at 45° will by turning the instrument

round (Fig. 173).
In Brewster's kaleidoscope there are only two mirrors, and the

FIG. 173. — Symmetrical images formed in the kaleidoscope.

name of catoptric chamber is ordinarily given to instruments which
contain three or more.

CHAP, re.] REFLECTION OF LIGHT. 257

The magic mirror is nothing more than a combination of two
plane mirrors inclined so as to reflect the images of objects separated
from the spectator by certain obstacles. It is used, under the name
of the polemoscope, during sieges, to observe the exterior movements
of the enemy, while the soldiers remain in shelter behind a parapet
(Fig. 174).

Some years ago a poor man was seen on the quay of the Louvre,
who showed to the amazed spectators the fa9ade of the Institute
through an enormous paving-stone. This magic-glass which enablea .-J ft ^

v<^-m.

IT?

FIG. 174.— Poleuioscope.

people to see through opaque bodies, was composed of a tube broken
in the middle, in which was placed a stone ; but the two pieces were
really united by tubes (in the supports) twice bent at a right angle,
and containing four plane mirrors inclined at 45°, as snown in
Fig. 175. The luminous rays could then, by following the bent
line, pass round the stone .and reach the eye.

Other instruments of much greater scientific importance than
those just mentioned are also based on the laws of reflection of
light from the surface of plane mirrors. But their description

258

PHYSICAL PHENOMENA.

[BOOK in.

would draw us beyond the limits to which we are restricted in
this first volume, and we shall confine ourselves to a simple men-
tion of them. They are the sextant, the goniometer, and the heliostat.
The sextant is used on board ship to measure the angular distances
of two distant objects ; for instance, a star and the moon's edge.
Goniometers are instruments employed to measure the angles made
by the sides of crystals ; and the name of heliostat is given to an
apparatus used to reflect the sun's rays in an invariable direction,
in spite of the daily movement of the earth, which causes that body
to pass over the heavens from east to west.

When light, instead of being reflected from a plane surface, falls
on a polished curved one, the laws of reflection remain the same for
each point of the mirror ; that is to say, the angles of reflection and
of incidence are always equal at each point, on either side the perpen-

FJQ. 175. — Magic telescope.

dicular to the plane tangent in the point, or from the normal to the
surface at the point of incidence : moreover, the incident ray, reflected
ray, and the normal, are in the same plane. But the curvature of the
surface modifies the convergence and divergence of the luminous rays
which, after reflection, fall on the eye : from this result particular phe-
nomena, and, in the case of luminous objects, the formation of images,
whose distance and position vary with the form of the mirrors, as also
with their dimensions and distances from the objects themselves.

Let us now study the phenomena of the reflection of light from
the surface of spherical, cylindrical, and conical mirrors.

CHAP. IV.]

REFLECTION OF LIGHT.

259

A section through a hollow metallic sphere gives us a spherical
concave mirror, if the concave surface is polished, and a spherical
convex mirror, if the convex surface is polished. If the spherical
portion is a tinned piece of glass, the stratum of tin is outside for a
concave and inside for a convex mirror. But we have already stated
why it is preferable to use mirrors of polished metal for the observa-
tion of physical phenomena. We shall speak here of these alone.

Let us observe what happens when a luminous object, for
instance, the flame of a candle, is placed at various distances from
a concave mirror in a dark room. We shall in these experiments

FIG. 176. — Concave mirror. Inverted image, smaller than the object.

place the luminous point in the axis of figure of the mirror, that is,
in the line which joins the centre of the sphere to which it belongs
to the middle or the top of the spherical segment.

Let us first place the light at a distance from the mirror greater
than the radius of its curvature. It will be easy, by the aid of a

x 2

200 PHYSICAL PHENOMENA. [BOOK in.

screen, to receive the reflected rays, and see that they form a smaller
and inverted image of the object at a point in the axis comprised be-
tween the centre of the sphere and the centre of the light-source
(Fig. 176). On moving the luminous source further from the mirror,
we must, in order to receive the image, approach nearer and nearer
to the screen from the point of the axis called the principal focus of
the mirror (we shall soon see why), and the inverted image will by
degrees diminish. If the candle is brought forward from its actual
position towards the centre, we observe that the image, still inverted
and smaller than the object, will gradually get larger as it approaches

FIG. 177. — Concave minor. Inverted images, larger than the object.

the centre. If the candle comes to the centre, the image will arrive
there at the same time, and will be blended with it in position and
size. If we now continue to bring the candle nearer to the mirror,
we cause the image to pass beyond the centre ; it becomes larger and
larger, always retaining its reversed position. In proportion as the
object approaches the principal focus the image increases in size and
becomes more and more diffused, until it is too large to be received on
the screen. When the source of light reaches the focus, the image is
situated at an infinite distance and has therefore practically vanished.
Thus far, the image of the luminous object has been real, that is,
it has actually existed in the air, at the point where it is formed,

CHAP, iv.] REFLECTION OF LIGHT. 261

and the reunion of the luminous rays has materially reproduced,
so to speak, the form and colour of the object. We have also been
able to receive this image on the screen. This is no longer the case,
however, if we place the luminous object at a less distance than the
principal focus of the mirror. The real image then exists no longer ;
but the eye still perceives behind the mirror, as in plane mirrors, an
image of the candle : this is called a virtual image. It is upright and
larger than the object, as shown in Fig. 178, and its apparent dimen-
sions go on diminishing, in proportion as the light is brought nearer

FIG. 178.— Concave mirror. Virtual images, erect and larger than the object.

to the mirror. It would have the dimensions of the object itself, if it
touched the reflecting surface. These various phenomena can be
easily observed by the concave mirrors used for the toilet, the curva-
ture of which is calculated in such a way that, at a short distance
from the mirror, the observer, who is at the same time the object,
finds himself in the position described in the preceding experiment :
in this case, he sees his figure increase or diminish. On going
further and further away from it, he will see reproduced, in inverted
order, the phenomena above mentioned.

262 PHYSICAL PHENOMENA. [BOOK in.

Let us now return to these phenomena, and see how the laws of
the reflection of light account for the various conditions which
•characterize them. For this purpose we must determine the path
which a ray or luminous pencil follows, when it is reflected from
the surface of the concave mirror.

Fig. 179 shows a cylinder of parallel, luminous rays, that is, rays
which have emanated from a point situated on the axis of the mirror
at a distance which may be considered as infinite. It is thus with
the light which comes from the sun, stars, or even, on the surface of
the earth, from an object at a distance, compared with the radius
of curvature of the mirror.

Both geometry and observation agree in proving that all such rays
when reflected cut the principal axis at a point situated at an equal

distance between the
centre c and the apex
A of the mirror. Their
reunion produces in F,
the principal focus, an
image of the point,
which the eye will per-
ceive there, since the

FIG 179.-Concave minor. Path and reflection of rays divergent ray 8 which

parallel to the axis. Principal focus. penetrate our organ

of vision will produce the same effect as if they issued from
a real luminous object, situated at the focus. The phenomenon
is the more exact as the surface of the mirror is smaller, that is,
as the angle of the cone, having its highest point at the centre
c of the mirror while its base is the mirror, is smaller. This
angle must not exceed 8 or 10 degrees. If the mirror is spherical,
the curvature is the same at each of its points; and the reflected
rays will then follow a similar path in relation to the secondary
axis, that is to say, to the right lines which join each point
of the mirror to the centre. There are endless secondary foci on
these axes, situated like the principal focus, at equal distances
between the centre and the mirror.

Figs. 180 and 181 show the path of the luminous rays, when
the object is situated at a distance which is not infinite, and which
lies near the mirror

CHAP, iv.] REFLECTION OF LIGHT. 263

The equality of the angles of reflection and incidence indicates
in these various instances how the points of convergence of the rays,
either on the principal or on the secondary axes, are situated at the
very points where experiments has shown us that the images are formed.

Indeed, if the luminous point is at s (Fig. 180), beyond the
centre of the mirror, a ray s I is reflected in I s and cuts the axis
between the centre (c)
and the focus. Bring-
ing the luminous point
now to the centre itself,
the rays fall normally,
and follow, after reflec-
tion, the course which
they at first took from

the light : the luminOUS FlG- 180.-Concave mirror. Conjugate foct

point and its focus then coincide. If the point still approaches the
mirror, but to a less distance than the principal focus, the reflection
takes place on the axis beyond the centre.

It is evident, and experiment also confirms the fact, that if the
path of a luminous ray is s I s (Fig. 180) from the object s to the
focus s, the path will
be exactly the reverse
when the ray starts
from the point s, so
that the points s and
s are alternately foci
one of the other. These
are called conjugate

fod. FIQ- 181. — Concave mirror. Virtual focus.

The conjugate focus of the principal focus is infinite; in other
words, the rays which emanate from this point are sent back parallel
to the axis of the mirror. At the points situated between the princi-
pal focus and the mirror, the focus is virtual, because the reflected
luminous rays are divergent (Fig. 181) : we can no longer therefore
consider them as conjugate foci.

Lastly, the two figures 182 and 183 show how, in the one case,
the images are real, inverted, and smaller than the object, and in
the other, upright, virtual, and larger than the luminous object. To

264

PHYSICAL PHENOMENA.

[BOOK in.

construct the images geometrically, and to account for their positions
and dimensions compared with those of the object, the images are
sought at each extreme point A, B. To this end we join A c, B c
(these are the secondary axes); then, the rays parallel to the

FIG. 182. - Concave mirror. Real and inverted image of objects.

principal axis are reflected to the focus F. The points of contact of
the reflected rays with the corresponding secondary axis give a and
b, images of the extremities of the object. This construction is
easily followed by means of the figures.

FIG. 183.— Concave mirror. Erect and virtual image of objects.

In convex mirrors, the foci and images are always virtual ; and
this fact is accounted for, if we follow the path of the rays and lumi-
nous pencils for each different point of a luminous object. We also
.see why, in these mirrors (Fig. 185), the image is upright and always

CHAP. IV.]

REFLECTION OF LIGHT.

265

smaller than the object. The dimensions, moreover, become smaller
as the distance from the object to the mirror augments. If the
surface of the mirror is very large, a disfigurement is observed,
which is more apparent as the surface is increased in extent. Any
one may see this by looking into the polished balls which are
placed in gardens, and in which the surrounding distant country
is reflected.

FIG. 184.— Upright virtual image in convex spherical mirror.

When we examine, in a spherical mirror, the path of the reflected
rays proceeding from a luminous point, situated on the axis at any
distance, we see that these rays successively cross each other, first on
the axis at its different points, then beyond the axis, in such a man-
ner that the points of intersection form a surface which geometers
call a caustic. At all the points of this surface the light is more
concentrated than elsewhere, and its maximum concentration is at

266

PHYSICAL PHENOMENA.

[BOOK in.

the focus of the given point. The caustic varies in form with the
position and distance of the luminous point ; but the existence of it
can be proved by experiment.

Place a screen of white cardboard, cut so as to take the form of

the mirror. When
this is exposed to the
light of the sun, or
to that of a lamp, we
perceive on some por-
tions of the screen
a brighter light, the
outlines of which in-
dicate the form of
the caustic, which is
evidently the same

FIG. 185. -Convex mirror Erect and virtual image. whatever may be the

position of the screen

as regards the centre. A circular metallic plate, polished inside,
and placed on a plane, would in the same manner indicate the

form of this curve for a
cylindrical mirror (Fig. 186).
This experiment is due to
Brews ter.

When a glass full of milk is
exposed to the rays of the sun,
or still better, as Sir J. Herschel
states, a glass full of ink, we
perceive on the surface of the
liquid a bright curved line ;
it is the intersection of the
caustic of the cylindrical con-
cave mirror, which the glass

forms with the limiting plane of the liquid at the upper surface
(Fig. 187).

In optics parabolic concave mirrors are largly employed. These
possess the property of concentrating rays parallel to the axis of the
parabola to the focus of this curve, whatever may be the angle of
the mirror, and they also send back in parallel lines all the light from

FIG. 186.— Caustic by reflection.

CHAP. IV.]

REFLECTION OF LIGHT.

267

a luminous object situated at the focus. Spherical mirrors only
produce this result when the surface is very small.

Concave or convex cylindrical mirrors produce images in which
the dimensions of the objects
are not altered in the direction
of the length of the cylinder;
but which, on the contrary, are
varied along in a direction per-
pendicular to the first, that is
to say, along the circumference
of a section. The rays reflected
along a line parallel to the axis
follow the path which they
would take in a plane mirror ;
those which are reflected on a
circumference follow the path
which their reflection from a
spherical mirror would produce.
If the cylinder is convex, the FIG. isz.-caustic by reflection.

images will always be narrower in the direction of its width ; if con-
cave, they will sometimes be narrower and sometimes wider according
to the distance of the object.

Fio. 188. — Cylindrical mirror. Anamorphosis.

2C8

PHYSICAL PHENOMENA.

[BOOK in.

In convex conical mirrors the reflected images are disfigured in
the direction of the circumferences, and as the degree of curvature
changes from the base to the apex, a narrowing in the dimensions ^
produced, which is more considerable as they approach the apex. If
the conical surface were concave, the form of the image would be
pyramidal, but for certain positions of the object it would be enlarged.

FIG. 189. Reflection on conical mirrors. Anamorphosis.

In both these mirrors the reflection of luminous rays always takes
place rigorously according to the laws which we have stated ; so that
we can take odd and deformed drawings, in which the eye cannot
distinguish any figure, which nevertheless, when reflected in cylin-

CHAP, iv.] REFLECTION OF LIGHT. 269

drical and conical mirrors, present a faithful representation of known
objects. The name of anamorphosis is given to this changing of
forms, and opticians have pictures which they sell with conical or
cylindrical mirrors, in which the lines and colours have been com-
bined to produce regular images of landscapes, persons, animals, &c.
(Figs. 188 and 189).

We have, in what has gone before, solely considered light reflected
regularly from the surface of polished bodies ; and the phenomena
produced by this reflection show sufficiently, as we have stated above,
that if the degree of polish were perfect, the reflecting body would be
invisible to us. We should see the more or less disfigured image of
the luminous objects which surround it, but we should not see the
mirror itself. And if, with the exception of the sources of light, all
bodies were in the same condition, we should only see an indefinite
multitude of images of luminous bodies, of the sun, for example,
without seeing anything else. In a dark room, if the solar rays fall
on a mirror, the surface of this latter gives a dazzling image of the
sun ; but the other points of the reflecting body are only slightly visible
by the irregularly reflected or scattered light. It is this light which
enables the mirrors to be seen from all parts of a dark room.

Fio. 190.— Light reflected very obliquely.

The proportion of specular and scattered light reflected by a body
varies with the polish of its surface, and also with the nature of the
body, its colour, and, lastly, with the angle of the incident rays. A
piece of white paper reflects light in every direction ; but its white-
ness is brighter the more perpendicularly it is exposed to the

270 PHYSICAL PHENOMENA. [BOOK m.

source of light. Moreover, if the observer is placed so that he can
examine the surface of the paper in directions more and more oblique,
the brightness of the scattered light diminishes, but by way of com-
pensation the eye receives an increasing number of rays regularly
reflected. It is for this reason that on placing the flame of a candle
very near the surface of a sheet of paper, and looking at it obliquely
towards the candle, a very distinct image will be seen of the reflected
flame as in a mirror.

When we say that scattered or diffused light is light reflected
irregularly, we do not mean that the rays of which it is composed
follow other laws, during reflection, than light reflected by mirrors.
The irregularity which it undergoes proceeds from the roughness of
the surface of the dull rough bodies, which receive the light under

varied angles of incidence and
disperse it in every direction.
When such a surface is looked at
very obliquely, the roughnesses
hide each other, and the rays
emanating from parallel sources
in the general direction of the
surface become more and more
numerous, which explains the
*"• 1«^S^^tS'S^SSt^^ li8'" increasing proportion of light

regularly reflected. That the

quantity of light reflected by means of mirrors varies with the
condition of their surface is not to be doubted. A piece of polished
glass becomes a mirror ; unpolished, it would scarcely scatter the
diffused light. Wood, marble, horn, and numerous other substances
are the same. But the reflecting power, if we give this name to the
property to reflect light to a greater or less extent, varies, with
equal degree of polish, according to the nature of the substances and
the angle of incidence. Of a hundred rays of light received by water,
glass, polished black marble, mercury, or speculum metal, with an
incidence of 50°, water reflects 72, glass 54, marble 60, and mercury
and speculum metal 70. If the incidence augments, the number of
reflected rays per cent, diminishes for the first three bodies in rapid
proportion, and at the most is no more than 2 or 3, at from 60° to
90° ; whilst, under this latter incidence, mercury reflects 69 rays out

Fia. 192. — The Ghost (produced by reflection).

CHAP. iv.J REFLECTION OF LIGHT. 273

of 100. Dark-coloured substances reflect only a little light. Lamp-
black does not scatter light, arid reflects but a small amount.

When light is reflected from a polished but transparent surface,
images are produced, but they are very feeble, as a great part of the
incident light passes through the substance. This is the reason why
mirrors and ordinary looking-glasses are tinned at the back, and the
images are thus formed on an opaque body of good polish.

But untinned glasses could be used, and they give good coloured
and very bright images when the objects which they reflect are well
lighted, and when the space which surrounds them is at the same
time in relative darkness and receives little or no diffused light.
Such is the principle of the fantastic apparitions known at theatres
as ' Ghosts ' (Fig. 192), and which have been recently used with
success in the drama.

The room in which the spectators are seated is in darkness,
and the stage, separated from the room by a sheet of plate glass,

FIG. 103.— Airangenunt of the uusilvercd glass and the position of .the Ghost.

is so slightly lighted up, that the glass is quite invisible. By giving
to this an inclined position (Fig. 193), it reflects the image of a person
who is strongly illuminated and stands under the front part of
the stage, called the first sub-stage. The actor is seen apparently
on the stage by the spectator as a virtual image, animated, and

274 PHYSICAL PHENOMENA. [BOCK in.

the actions of the performer can thus be seen in a way to delude
the spectators and make them believe in the appearance of a real
intangible phantom. The necessity of giving to the glass an inclined
position, in order to make it retiect, causes the ghost to appear
inclined towards the spectators, and this defect is especially per-
ceptible to the spectators sitting at the sides.

CHAP. V.]

REFRACTION OF LIGHT.

275

CHAPTEE V.

REFRACTION OF LIGHT.

Bent stick iu water ; elevation of the bottoms of vessels— Laws of the refraction
of light; experimental verification — Index of refraction — Total reflection —
Atmospheric refraction ; distortion of the sun at the horizon.

WHEN a straight stick is thrust into clear water, that part of
it which is beneath the liquid does not appear to be continued
in a straight line. The stick seems to be bent from the surface of
the water, and the end which is immersed rises as if it had

FIG. 194. — Phenomena of refraction of light. The bent stick.

diminished in length. If the stick is placed vertically, or if the
eye receives the visual rays in a direction which causes it to be
seen as if it were vertical, the stick no longer appears bent, but

I 2

276 PHYSICAL PHENOMENA. [BOOK m.

simply shortened. This phenomenon is easily shown by putting
the end of a pencil into a tumbler full of water.

If before filling a vessel with transparent liquid we look at the
bottom of the vessel over the edge from a fixed position, and if,
without removing the eye from its place, water is poured gently in,
the bottom of the vessel appears to rise gradually, and at last seems
much higher than before.

To make this experiment more striking, put a piece of money on
the bottom of the vessel in such a position that the edge of the
vessel entirely hides it. As the level of the water rises the object
becomes visible and appears to rise with it, and takes the apparent
position indicated in Fig. 195.

FIG. 195. — Refraction of light. Apparent elevation of the bottoms of vessels

We have all, moreover, noticed that objects seen through a flask
of clear water appear enlarged, distorted, and removed from their
real position. If we follow the movements of fishes as they swim
about in glass globes, it is surprising to see these animals, sometimes
disappearing, sometimes becoming considerably larger, and sometimes
gradually diminishing, until we see them in their actual dimensions.

All these phenomena are due to what physicists call the refrac-
tion of light — that is to say, to the deviation which luminous rays
undergo when they pass obliquely from one medium into another,
for example, from air into water.

When light leaves a luminous or illuminated object it moves in
a right line — as we have just seen — provided that the medium
through which it passes is homogeneous. Thus the rays which
enable us to see the end of the stick in the water are rectilinear
so long as their passage is through the water, which is a homogeneous
medium. The path followed by the same rays in leaving the liquid
surface and passing to our eye is likewise rectilinear, because it

CHAP, v.] REFRACTION OF LIGHT. 277

takes place through another homogeneous medium. But the second
direction is not a continuation of the first, and the complete course
followed by the luminous rays forms a broken line, the angle of
which will be found at the point of incidence, at the separating
surface of the two media.

Similar phenomena are seen in all kinds of liquids, in trans-
parent solids like glass, and also in gases ; only, as we shall presently
see, the deviation varies with the nature of the medium.

The principal phenomena connected with the refraction of light
were examined long ago, and the appearance of objects when seen
through clear water was doubtless observed in very remote ages.

The ancient astronomers, Ptolemy for example, noticed the effects
of atmospheric refraction, that is, the deviation .which the luminous
rays from the stars undergo in passing from the vacuum of planetary
space through the denser medium of our atmosphere. But it was not
until the commencement of the seventeenth century that a young
Dutch geometer, Willebrod Snell, discovered the cause of this devia-
tion, and the laws which govern the passage of a luminous ray when
it passes obliquely from one homogeneous medium to another. These
laws sometimes bear the name of Descartes, because this great man
discovered them in his turn, or at any rate explained them under a
form which is still retained in science.

Let us examine the nature of these laws. In order to prove them
experimentally, a ray, or a bundle of rays, is caused to fall obliquely
on the surface of a liquid contained in a semi- cylindrical glass vessel
placed within a graduated circle, and the angle which the path of the
ray makes with the vertical is then measured : this is the angle of
incidence. The ray enters the liquid, is then broken or refracted, and
is seen to approach the vertical line. The angle of refraction is
smaller than the angle of incidence.

If we vary the angle of incidence, the angle of refraction varies
also ; and we do not at once perceive the relation which exists
between these variations. But because the refracted ray is always
in the plane of the graduated circle as well as the incident ray, —
and it is the same with the vertical, — it follows that the first law
is as follows: —

When a luminous ray passes obliquely from one medium into
another, it is bent aside, and both the incident and the refracted ray

278 PHYSICAL PHENOMENA. [BOOK ITT.

remain in the same perpendicular plane, normal to the surface of sepa-
ration of the medium. We may also add, that if the ray of light
enters perpendicularly to the surface, it continues its path in the
same direction. There is no refraction for the normal incidence.

Fig. 196 represents the instrument as arranged for proving the
second law.

The incident ray coming from the sun, for instance, falls at I on
a mirror inclined in such a manner as to reflect it in the direction

FIG. 196.— Experimental demonstration of the laws of refraction.

of the centre through a little hole in a diaphragm. An index,
furnished with a point at its extremity, indicates the direction of the
incident ray, and the line o' a can be measured on the horizontal
divided scale, which can he moved up or down. This line, or, better,
its relation to the length of the ray o' a, is what geometers call the
sine of the angle of incidence. Another index, also furnished with a
diaphragm pierced with a hole, receives the refracted luminous ray
after its passage through the water, and o' b is measured on the scale,
which gives the sine of the angle of refraction. Let us observe that

CHAP, v.] REFRACTION OF LIGHT. 279

the luminous ray, on emerging from the water into the air, does not
undergo a new refraction, as it passes out by an incidence normal
to the surface of the cylindrical vessel.

Let us suppose that the first observation gives us two sines, such
that, by dividing that of the angle of incidence by that of the angle of
refraction, the quotient is 1/335. If we repeat the experiment several
times, changing the direction of the incident ray, we find that in each
fresh experiment the quotient of the sine of incidence by that of re-
fraction will continue to be 1/335 ; and it will be the same as long as
the two media are air and water. But this number, which is called
the index of refraction, varies when one of the media is changed or
when both change ; thus, from air to glass the index of refraction is
no longer equal to that from air to water. It has also been found
convenient to calculate the indices of all transparent bodies, on the
supposition that the light passes from a vacuum into each of them.
By this means absolute indices are obtained. Generally speaking,
the refraction increases with the density of the second medium,
although there are many exceptions. Thus, the refractive power of
a medium very usually increases with its density.

The second law of refraction of light may be thus stated : —

For the same two media, the quotient of the sines of the angles of
incidence and refraction is a constant number, whatever the incidence
may be.

The laws we have just studied indicate the path which light
follows when luminous rays pass
from one medium to another. But
this path, as both reasoning and
experiment prove, remains the same
if the light passes from the second
medium into the first. Then the
incident ray becomes the refracted
ray, and vice versa. For example,
if the luminous point is in the water
at s, the ray which falls at the point
I of the surface will be deviated
from the perpendicular, following Fl°-

the direction I R ; the path SIR will be the same, only reversed, as
if the incident ray had been at R I ; so that the angles of incidence

280

PHYSICAL PHENOMENA

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and refraction will have inverse sines, the quotient of which, how-
ever, will be always constant.

These laws account for the phenomena described at the commence-
ment of the chapter. The eye
which examines the end of a
stick in water, sees it by means
of the luminous rays which
this extremity sends to the sur-
face ; which rays are refracted
the more as their incidence is
more oblique. Tlie phenome-
non is therefore the same as if
the luminous point were situ-
ated at the point of conver-
gence 01 these rays, and the
the stick in this point. The

FIG. 198.— Explanation of the bent stick.

eye in reality sees the end of

FIG. 199.— Apparent elevation of the bottoms of vessels ; explanation.

same effect is produced for all intermediate points, and the stick
appears bent The same explanation accounts for the elevation of

CHAP, v.] REFRACTION OF LIGHT. 281

the bottoms of vessels filled with liquid. Even when we look at
the bottom in a perpendicular direction, the effect is produced,
because the eye does not receive a single ray, but a bundle of rays,
which diverge more on passing through the air, on account of re-
fraction, than through the liquid. The point then appears to rise
towards the surface from o to o' (Fig. 199).

A singular phenomenon called total reflection results from the laws
of refraction, which may be proved by experiment. Let us imagine a
luminous point placed in water, at the bottom of a vessel. This point
sends out rays of light in every possible direction at the surface of
separation of the air and water. Now, do all these rays emerge ?
We shall see that this is impossible, and that there is a certain angle,
variable with the nature of the medium, beyond which the luminous

FIG. 200.— Total reflection. Limiting angle.

ray cannot penetrate into a less refractive medium. Indeed, since the
angle of refraction is greater than the angle of incidence, a moment will
arrive when the first angle having become a right angle, the angle of
incidence 0 I N' is still less than a right angle. The refracted ray no
longer emerges ; it grazes the horizontal surface of the liquid. Beyond
this, the angle of incidence always increasing, the angle of refrac-
tion would become greater than a right angle. In this case the ray
returns into the liquid, and is reflected, according to known laws, to
the inner surface of separation. As in the least incidences the emer-
gence is not complete, and there is a partial reflection of the rays, so
when the emergence is nil, there is said to be a total reflection. All
the luminous rays which, coming from 0, cut the surface of separation

282

PHYSICAL PHENOMENA.

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of the two media, are thus divided into two portions : the first,
containing those which emerge, forms the cone of refracted rays ; the
second is composed of all the rays which cannot emerge, and which
are therefore reflected back into the interior of the more refractive
medium.

Fitt. 201. — Phenomenon of total reflection.

We name the limiting angle that beyond which the total reflection
commences. This angle is about 48£° for rays which are refracted
from water into air, while it is only 41° from glass to air.

A very simple experiment proves the phenomenon of total

CHAP. V.]

REFRACTION OF LIGHT.

283

reflection, and, at the same time, shows that reflection thus obtained
exceeds in brightness all those which are obtained directly; for
example, at the surface of mercury or polished metals. A glass of
water is held in such a position that the surface of the liquid is
above the eye (Fig. 201). If we look obliquely from below at this
surface, it appears brighter than polished silver, and seems to possess
a metallic brilliancy. The upper part of an object plunged in the
water is seen reflected as in a mirror.

A diver immersed in perfectly still water, and having his eyes
directed towards the surface of the liquid, would witness singular
phenomena. Kefraction will cause him to see, in a circle of about
97 degrees in diameter, all the objects situated above the horizon,
more distorted and narrowed, especially in height, as they approach
the sensible horizon. " Beyond this limit, the bottom of the water
and the submerged objects would be reflected, and would be pictured
to the sight as distinctly as by
direct vision. Moreover, the
circular space of which we
have spoken would appear to
be surrounded by a perpetual
rainbow, coloured slightly, but
with much delicacy." (Sir J.
Herschel.)

The phenomenon of total
reflection also explains how it
happens that an isosceles and
rectangular glass prism, fitted
to the opening of the shutter
of a camera obscura, intercepts
all the light coming from the
outside, and leaves the room

in the most complete obscurity. The rays which enter the prism
by its perpendicular side do not suffer refraction, but when they
have arrived at the oblique surface, the angle of incidence is 45
degrees; that is to say, greater than the limiting angle. The total
reflection takes place, and there is no emergence. The rays which
alone could enter would be due to oblique incidences which are
prevented by the tube containing the prism.

z 2

FIG. 202.— Phenomenon of total reflection, in the
shutter of a camera obscura.

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PHYSICAL PHENOMENA.

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The phenomenon of refraction occurs whenever a ray passes
obliquely from one medium into another, provided that they differ in
nature and density. It is evident, then, that the luminous rays
emanating from planets, the sun, the moon, and fixed stars, which, after
having travelled through the celestial space, have to traverse the strata
of our atmosphere before reaching the eye, are subjected to refraction.
Hence then we do not see these bodies in the direction of the right
lines which really join each of them to the position which we occupy
on the surface of the earth. There is no exception except for those
situated at the zenith of each horizon. Atmospheric refraction
depends on the angular height of the body observed above the
horizon ; it depends, likewise, on the law which regulates the decrease

FIG. 203. — Atmospheric refraction. The effect on the rising and setting of stars.

of density of the strata of air constituting the atmosphere. As we
have at present very uncertain data concerning this law, it would be
very difficult to measure directly the deviations which correspond to
the various heights of bodies. Happily, astronomy has come to the
help of physics. As the angular distance of a star from the celestial
pole remains invariable, it follows that, whatever may be the height
to which the diurnal movement brings it above the horizon, the differ-
ences, which observation indicates between the distances obtained
from the greatest elevation and at the horizon, can only proceed from
atmospheric refraction. Hence it is possible to construct a table of
astronomical refractions from the horizon to the zenith.

CHAP, v.] REFRACTION OF LIGHT. 285

At the horizon the refraction is nearly 34'. As the diameters
of the sun and moon have a less value, it follows that at sea, when
no object hides the horizon, the disc of the sun at sunrise will
appear entirely above the liquid surface before the top of that*
luminary has emerged above the real horizon. The day is thus
found lengthened in the morning by refraction, and the same thing
happens in the evening with the setting of the sun.

The same phenomenon accounts for the peculiarity observed
in many eclipses of the moon, that the latter body is seen eclipsed,
while the sun, whose light the earth, interposed between it and the
moon, is cutting off, is still visible above the western horizon. Lastly,
it is atmospheric refraction which, in total eclipses of the moon, allows
a certain number of solar rays to reach our satellite, preventing
its disc from being completely invisible. This disc, then, presents a
very marked reddish colour, similar to the tint of the atmosphere
at sunset.

286 PHYSICAL PHENOMENA. [BOOK in.

CHAPTER VI.

REFRACTION OF LIGHT. — PRISMS AND LENSES.

Transparent plates with parallel faces ; deviation of luminous rays — Multiple
images in a silvered mirror — Prisms — Phenomena of refraction in prisms —
Converging and diverging lenses — Real and virtual foci of converging lenses ;
real and virtual images — Foci and images of diverging lenses — Dark chamber
— Megascope — Magic lantern and phantascope — Solar microscope.

WHEN a luminous point is examined through a plate of trans-
parent substance, glass for instance, the two plane faces of
which are parallel, if the eye and the luminous point are on the
same perpendicular in regard to the plate, the luminous point is
seen in the direction where it would be seen without the inter-,
position of a refractive medium. This is the case because there is
no refraction for normal rays, that is for rays falling perpendicularly
on a surface.

Ho 204.— Normal View. FIG. 205.— Oblique View.

Deviation due to refraction through plates with parallel faces.

But the same result does not take place in the case of an
oblique incidence, for then the position of the luminous point is
altered, and the deviation may be rendered evident by a very

CHAP. vi. J REFRACTION OF LIGHT. 287

simple experiment. Take a sheet of glass, place it upon a piece
of paper, upon which straight and curved lines have been drawn
in such a manner that the glass only covers one part of the lines.
If we look at it perpendicularly, we shall observe that the lines seen
through the glass are a continuation of the lines seen by direct
vision. If we look at it obliquely, we shall notice a deviation,
a solution of continuity, the more marked as the incidence of the
luminous rays is more oblique. This deviation is due to refraction,
and it increases with the thickness of the plates.

It evidently follows from this that transparent plates, such as
window-panes, and the glass used to cover engravings, distort the
images ; but this defect is scarcely perceptible, and is rarely
remarked.

When we speak of deviation, we mean lateral displacement, for
the luminous ray which traverses one or more plates with parallel
faces, preserves after its emer-
gence a direction parallel to that
of the incident ray, as shown in
Fig. 206. This property is a con-
sequence of the parallelism of the
normals to the points of incidence
and emergence as well as of the
law of refraction for two media,
the refractive power of which FlG 206_Path of a luminoug pencil-

is known. Experiment proves

that the rays are always parallel when they emerge, after having
traversed any number of plates, even when these plates are not
formed of the same substances and when they are not all parallel
to each other ; and theory foresaw this result. Again the same result
is produced when plates of different substances are so arranged.
The lateral displacement depends, in every case, on the refractive
power of the substances and the thickness of the plates.

If we place a candle in front of a silvered mirror, and hold
it obliquely so as to examine the image, we shall perceive, before
the bright image formed on the inner silvered face, a more feeble
image proceeding from the outer face of the glass, and also a
series of images still less brilliant behind the first. These latter
images are due to the rays which, after being refracted the first

288

PHYSICAL PHENOMENA.

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time in the thickness of the plate, are partially reflected by the
silvered surface and by the interior surface of the external plane

FIG. 207.— Multiple images produced by FIG. 208.— Path of the rays which giye place to the

refraction in plates with parallel faces. multiple images of plates with parallel faces.

FIG. 209.— Geometrical form of the prism.

FIG. 210. — Prism mounted on a stand.

of the mirror. Fig. 208, which gives the successive path of these
rays, accounts for the phenomenon we have just described.

CHAP. VI.]

REFRACTION OF LIGHT.

289

We will now examine the phenomena which depend on the
refraction of light when it traverses a refractive medium, the plane
faces of which are not parallel, that is to say, in prisms.

Fig. 209 shows both in perspective and in section the geometrical
form of a prism as used in optics. For the convenience of experi-
ment the prism is mounted on
a stand, in such a manner that
it can be turned round or in-
clined at will (Fig. 210).

The effect of a prism on a
luminous ray, which enters ob-
liquely at one of its faces, tra-
verses the prism, and emerges
from the other face, is to de-
viate the ray towards the side
which constitutes the base. It
is sufficient for us to examine
Fig. 211, which shows the path
of the incident and refracted
rays, to prove this : the inci-
dent ray s I after the first re-
fraction takes the path I E in
the prism, is again refracted
on emerging from the prism,
and finally issues in the direc-
tion E R. This is confirmed by
observation, for if we examine
an object through a prism, by
placing its edge in a horizontal
position, the image appears
raised up, if the base is be-
low ; and it is lowered, if the base occupies the reverse position. In
fact, the eye sees the luminous points in the direction of the rays
which leave the prism. If, as we have just seen, the bundle of rays
diverges and approaches the base of the prism, their convergence
will take place towards the summit, and the eye will see the
point raised or lowered according as the base is above or below
the opposite angle.

FIG. 211. — Deviation of luminous rays? by prisms.

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PHYSICAL PHENOMENA.

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The deviation of the rays increases with the angle of the prism,
when the angle of incidence of the rays remains the same. For
the same prism, in proportion as the incident ray approaches the
normal the angle of emergence increases, and there is a direction
in which the rays attain the limiting angle of total reflection,
when there is no more emergence. This depends, of course, on
the substance of which the prism is composed.

PIG. 212. — Images of objects seen through prisms.

In the case of a glass prism of 45°, all rays which fall below
the normal towards the base cannot emerge ; but those which fall
towards the summit become emergent rays. If the angle of the
prism is double, that is to say, a right angle, no luminous ray,
whatever may be its incidence, can emerge out of the prism; so
that such a prism, with a blackened base, if placed at the opening

CHAP, vi.] KEFRACTION OF LIGHT. 291

of a shutter in a dark room in a transverse position, and so as
to close the opening, would allow no luminous ray to enter.

We shall presently describe other phenomena of great interest,
obtained by the aid of prisms, through which rays from different
light-sources pass ; phenomena which show that white light is
formed of a multitude of rays of different colours, each being
refracted in a different degree. This is called the decomposition
or dispersion of light. But having now dealt with deviation, we
must first consider the path of a ray when it traverses transparent
media with curved surfaces.

LENSES.

If we construct of glass, or of other transparent substance, a
disc with two convex faces, that is to say, two segments of a
sphere with their bases in conjunction, we have what is called a

FIG. '213. — Magnifying glass or lens with convex surfaces, side and front view.

lens. The name is taken from the resemblance which exists between
the form of such a mass and that of the well-known vegetable —
the lentil.

There are various kinds of lenses; that which we are about to
describe, which forms the instrument called the magnifying glass,
is used by almost every one, as for instance naturalists, engravers,
watchmakers, &c., who wish to enlarge the smallest parts of objects
so as to be able to see them in detail.

There can be no doubt that glass lenses and their magnifying

202

PHYSICAL PHENOMENA.

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effects have been known for ages. Analogous objects have been
found in the ruins of Nineveh, Pompeii, and Herculaneum. Spec-
tacles have been used in Europe since the beginning of the
fourteenth century. But it is only for the last three hundred
years that the knowledge of the laws of refraction has enabled
opticians to construct and to combine lenses so as to obtain various
desired effects with accuracy.

Physicists have extended the name of lenses to all transparent
masses, terminated, at least on one side, by curved, spherical, or
cylindrical surfaces, even when these surfaces are concave instead of
convex, as in the magnifying-glass. More often, and indeed when-
ever the contrary is not stated, the surfaces of lenses are both
spherical ; or one may be plane, and the other spherical. "We shall
thus regard a lens throughout this work. All lenses may be con-
veniently grouped in two classes, according to the path which the
light which traverses them follows. Some, as in the magnifying-glass,

Fio. 214. — Converging lenses. — Bi-convex lens ;
plano-convex lens ; converging meniscus.

Fio. 215. — Diverging lenses. — Bi-concave lens;
plano-concave lens ; diverging meniscus.

are converging, that is to say, the luminous rays after their passage
through the lens are drawn together ; others are diverging, because,
on the other hand, the rays become more distant from each other, or
diverge either on entering, or issuing from, the refractive medium
of which they are formed. These can be very simply distinguished
at first sight, for converging lenses are always thicker at the centre
than at the circumference, while diverging lenses are thinner at
the centre than at the circumference.

CHAP. VI.]

REFRACTION OF LIGHT.

293

The type of converging lenses is the magnify ing-glass or bi-convex
lens, the two surfaces of which, generally of the same curve, are
convex. Next we have the plano-convex lens, one surface of which
is plane, the other convex. Lastly, the third converging lens is the
converging meniscus, one surface being concave and the other, a
more decided curve, rounded or convex. Fig. 211 gives the form
of each of these lenses seen edgewise, supposing the section to
be made in the direction of the diameter.

The type of diverging lenses is the bi-concave, formed of two
concave surfaces. Next, the plano-concave lens, one surface being
concave, the other plane ; and the diverging meniscus, the two sur-
faces of which are, one convex, the other concave, this latter having
a sharp curve.

We may also state that the principal axis of a lens is the
right line which passes through the centres of the spheres to
which their surfaces belong, or, if one of these is plane, the line
which, from the centre of the curved surface, falls perpendicularly
on the plane surface. In converging lenses, the axis passes through
the lens at its greatest thickness; while with divergent lenses it
passes where the lens is thinnest.

Without the aid of experiment, the known laws of refraction
indicate to us that a ray of light
which is propagated in the direction
of the axis will traverse the lens
without deviat'on, and will continue
its path in the line of the axis,
exactly as if it normally traversed
a plate with parallel faces.

There are other lines which have
an analogous property, and which are
called secondary axes. They are those
lines which cut the principal axis at
the middle of the maximum or mini-
mum thickness : I 0 i' (Fig. 216) is a secondary axis in each of the
lenses represented. When a luminous ray N I on entering follows the
direction of one of these lines, it emerges in a direction N' i' parallel
to that of the incident ray; and as the thicknesses of lenses are
generally very small, it may be said that the incident ray and the

FIG. 216. — Secondary axes of lenses.
Optical centre.

294 PHYSICAL PHENOMENA. [BOOK in.

emergent ray pass in the direction of the secondary axis. The
optical centre of a lens is the point where the principal axis and
the secondary axes meet. The optical centre is still in the
interior, if the two surfaces have not the same curvature, but it is
no longer situated at an equal distance from the two surfaces. For
plano-convex and plano-concave lenses, the optical centre is on the
curved surface ; in the converging and diverging meniscus lenses
it is outside the lens.

These definitions being understood, let us now examine the path
of light through a bi-convex lens. If we place it facing the sun, so
that its principal axis is parallel to the rays of light issuing from that
luminary, and then receive the light which emerges from the lens
on a screen \ laced a short distance on the other side of it, we shall

FIG. 217.— Path of rays parallel to the axis. Principal focus

perceive on the screen a luminous circle, the clearness and dimen-
sions of which depend on the distance of the screen from the lens.
When we move it further away or nearer to the screen, we find a
position when this brightness will be at its maximum, and the
clearness of the circular image will be greatest and its magnitude
the least. This would be a mathematical point, if the source of
light were itself a point. This point, to which the parallel rays
converge after their refraction to the principal axis, is called the
principal focus of the lens. The distance F A from the focus to
the lens, which is called the principal focal distance, depends both
on the substance of which the lens is made and on the curvature
of its surfaces. The greater the curvature, the less is the focal
distance, which is expressed by saying, that the lens is of short
focus.

CHAP. VI.]

REFRACTION OF LIGHT.

295

If a lens is placed in the opening of a dark room, the con-
vergent path of the sunlight can be traced in the air, because the
luminous cone renders evident the particles of dust which fly about
in the room.

The convergence of luminous rays produced by bi-convex lenses
readily explains the path of refracted light through a prism. The
effect produced by this latter medium is to cause the luminous ray
to approach the base of the prism. Now, a bi-convex lens may
be considered as an assemblage
of superposed prisms, the angle
being more acute as it approaches
the principal axis, while the de-
viation is greater as the angle
is more obtuse. Fig. 218 shows
this convergence, and experiment
agrees with theory in showing
that the point of meeting is on
the principal axis, provided that
the rays are very near the axis.

Let us examine the different
circumstances which result,
when the luminous point s
(Fig. 219) is near the lens, and
in the principal axis. The ex-
planation is the same, when the
luminous rays, instead of start-
ing from a point situated at an
infinite distance, proceed from
a light situated on the axis
at a finite distance. Only, in

this case, the focus does not coincide with the principal focus. As
long as this point is on one side of the lens, beyond its focal distance,
its focus s is formed on the axis beyond the principal focus, and
the more it approaches, the more distant is the focus. If it should
happen to be at the distance from the lens of double the focal
distance, the corresponding focus is precisely at the same distance.
If it again approaches the lens, the focus continues to recede, until
the luminous point, attaining the focal distance itself, its focus

Fio. 218.— The lens may be considered
as an assemblage of prisms.

296

PHYSICAL PHENOMENA.

[BOOK in.

disappears, or in other words it is situated at an infinite distance,
the rays leaving the lens parallel.

Hitherto the convergence of luminous rays has been really
effected after their departure from the lens; the focus is real;
which it is easy to prove by receiving the luminous cone on a
screen where the concentrated rays will produce an image of the
object, — a luminous point, for instance, if the object itself is a
luminous point. Again, the two points of the axis where we find
the object in one part, and the focus in another, are reciprocal

Fia. 219.— Path of rays emanating from a luminous point on the axis. Conjugate foci.

one to the other, that is to say, if the focus becomes the luminous
point, the first position of the luminous point marks the new
focus (Fig. 219). This is the reason why physicists give to these
points, the focal distance of which can be found by calculation,
the name of conjugate foci. The same fact has been proved in the
case of mirrors.

The luminous point s approaches from the principal focus towards

the lens, till its dis-
tance is less than the
focal distance (Fig. 220)
Then, the luminous
rays, after emergence,
recede from the axis or
diverge, so that there is
no longer a real focus.
It is now no longer
possible to collect the
divergent beam on a screen ; but the eye sees the luminous rays

FIG. 220. — Path of rays emanated from a point situated between
the principal focus and the lenses. Virtual focus.

CHAP, vi.] REFRACTION OF LIGHT. 297

as if they emanated from this focus, and the impression they receive
is that of the image of the luminous point.

The nearer the object approaches the lens, the more does the
image itself approach it ; and when the object comes into contact with
the transparent surface, the image arrives there at the same time.

These results can be proved both by calculation and experiment.
Let us examine, experimentally, images both real and virtual, which
are formed at the focus of a bi-convex lens or, in general, of a
convergent lens, when it is placed opposite a luminous object.

We have already seen how the image of an object whose
distance may be considered as infinite, and which sends to the
lens a beam of parallel rays, is formed : it is thus that the sun
produces an image in the principal focus of the lens.

FIG. 221. — Real image, inverted, and smaller than the object.

If the object A B is at a finite distance, more than double of
the principal focal distance, it will be real, inverted, and smaller
than the object.

This may be proved by receiving the image of a lighted
candle on a screen which we can move nearer or further away
from a lens, until we obtain a perfectly clear image. As the
distance of the candle diminishes, the image, which is always real,
will recede and become larger, until it is of precisely the same
size as the object itself. If the distances are measured which
separate the lens from the screen and from the candle, they are
found to be equal, and each is doiible that of the principal focal
distance. As the candle continues to approach the lens, the real
image enlarges and recedes; and it is then larger than the object
(see Figs. 222 and 223). We must increase the distance of the

A A

298

PHYSICAL PHENOMENA.

[BOOK in.

screen if we wish for clearness, but it will be seen that the brightness
diminishes, which is explained by the dispersion of the luminous
rays proceeding from the lens on a surface which increases quicker
than the quantity of light received.

FIG. 222.— Heal image, inverted, and larger than the object.

When the candle has arrived at the focal distance, the image
disappears; and this is easily explained, for as the rays issue parallel
to the axis, there can no longer be convergence. Thus far, the

FIG. 223. Image of an object situated at a distance from the lens greater than the principal

focal distance, and less than double that distance.

image has always been real; mother words, it has always been possible
to receive it on a screen ; its existence has been independent of
the observer. This will no longer be the case if we continue to

CHAP. VI.]

REFRACTION OF LIGHT.

299

advance the candle or other luminous object towards the lens ; for
then the screen placed at any distance will only give diffused light.
If, however, instead and in place of the screen, we substitute our eyes>
we shall see through the lens an image of the candle, no longer
inverted, but erect and magnified. How then does it happen that
the eye receives the sensation of an image which is not then real ?

FIG. 224.— Erect and virtual images of an object placed between the principal focus and the lens.

The luminous rays which each of the points of the object sends
to the lens issue from the refractive medium in a divergent form.
The eye which receives them undergoes the same sensation as
if it were acted upon by rays emanating directly from luminous
points situated on the other side of the lens, but at a much .greater

FIG. 225.— Principal virtual. focus of diverging lenses. -

distance than the object to which they belong. Hence; the increase
of apparent dimensions ; and also, the direction of the image, which,
becoming virtual, ceases to be inverted (Fig. 224). In this
instance, in proportion as the object approaches the lens the image
diminishes, until it touches one of the surfaces of the lens, when
the image becomes sensibly equal to the object itself. These are
the images produced by converging lenses.

A A 2

300 PHYSICAL PHENOMENA. [BOOK in.

Diverging lenses have no real focus. For example, in the case
of a bundle of rays parallel to the axis — which occurs when the
luminous point is situated on the axis at an infinite distance — in
issuing from the lens the rays diverge ; their point of intersection
is situated on the axis in front of the lens, and is called the principal
focus, a focus which is no longer real but virtual. The eye which
receives the divergent beam emerging from the lens experiences
the same sensation as if there was actually a luminous point at
the focus.

Diverging lenses do not produce a real image, because the
luminous rays, on emerging from a refractive medium, are separated
from each other, and have no effective point of union. But if we
apply to them the treatment before adopted in the case of the

erect and virtual image
given by a converging
lens, we perceive that
the images of diverging
lenses are likewise vir-
tual and erect. But
there is this differ-
ence, viz., that their

FIG. 226,-Erect virtual images smaller than the object apparent dimensions

are always less than

those of the objects which they represent. Fig. 226 indicates
the cause of this, and enables us to understand why images which
become smaller as the object is more distant, attain the size of
the object itself when this latter touches the lens.

Both converging and diverging lenses are used in the construction
of numerous optical instruments, in astronomical telescopes, micro-
scopes, lighthouses, &c.

We have described the most important of these in the volume
which treats of the "Application of Physics," and shall see how
wonderfully science is concerned in these operations. We shall
here confine ourselves to the construction of the most simple
instruments, in which real images are caused to produce various
optical effects; these are principally the camera obscura, the
megascope, the magic lantern, the solar microscope, and the
phantascope.

CHAP. VI.]

REFRACTION OF LIGHT.

301

In considering the propagation of light in right lines, we have
seen that if a small hole is made in the shutter of a perfectly
dark room the image of exterior objects is thrown on the
screen. This inverted image is only distinct in the case of distant
objects. To obviate this inconvenience and to give brightness
to the images, Porta conceived the idea of receiving the light on

Fio. 227.— Camera obscura.

a spherical concave mirror, which reflects both the rays and the
image on the screen. But he also obtained effects much more
remarkable, by placing a converging lens in the hole of a shutter,
when the images of outer objects were found to be given with
distinctness on a screen, the distance of which from the opening
of the shutter varied with the distance of the objects themselves.
It is easy to determine this distance by moving the screen back-
wards and forwards. Designers employ this dark chamber, in
order to trace on paper the outlines of a landscape they may wish
to produce. They make use of it in the form indicated in Fig.
227. Instead of a lens, they use a prism (Fig. 228), the side of

302

PHYSICAL PHENOMENA.

[BOOK in.

which, turned towards the object, is convex, and, by total reflection
from its plane surface, which is inclined at 45°, it projects the
beam of light upon the table, on which is
placed white paper. The image thus formed
is perfectly clear, and the draughtsman has
nothing to do but follow the outlines in
pencil. This modification of the camera
obscura is due to M. C. Chevalier, the optician.
The megascope is a dark chamber used
for the purpose of reproducing an object on
a large scale, such as a statuette, or picture.
Fig. 229 will save us a more detailed descrip-
tion. We may remark that, as the bright-
ness of the object is enfeebled by the dis-
persion due to enlargement, a mirror is used

FlG' camTra^cui-r °f ^ t0 Pr°Ject tne SUn'S rays °n tne Object, and

to obtain a sufficiently intense light.

The magic lantern is a megascope in which the object is
illuminated by means of a reflecting lamp. By the use of this

FIG. 229.— Megascope.

apparatus, the Enlarged images of pictures painted on glass with
transparent colours are projected on a screen. The tube through

CHAP, vi.] REFRACTION OF LIGHT. 303

which the inverted drawings are placed incloses a system of two
lenses, one plano-convex, the other bi-convex, which produce an
erect image on a screen in front of the instrument. By using
Drummond's light to illuminate the objects, far more brilliant
images are obtained ; and, by moving the screen further away and
bringing the lenses nearer together, the images can be greatly
enlarged.

Towards the end of the last century, a Belgian physicist,
Eobertson, obtained an extraordinary success by exhibiting, in
public, apparitions of phantoms, which, in the profound darkness
surrounding the spectators, appeared gradually to advance into the
middle of the room, and to increase in size. This was done by
means of an apparatus called a phantascope, analogous to the magic
lantern, that is to say, consisting of a box, containing a reflecting
lamp, and furnished with a tube having the same system of two
lenses to project the
image of a drawing
on a screen placed
in front of the in-
strument. But in
this case the lantern
is supported by a
moving table, one of
the feet of which FIG m _Magic lautern>

has a pulley com-
municating its movement to the lenses through the intervention
of an eccentric and lever. When the table moves further from the
screen, the plano-convex lens approaches the convex lens, the
image increases, and the illusion is produced in a much more com-
plete manner than by the aid of a movable diaphragm ; the light
which the image receives varying in proportion to its size. Eobertson,
who owed the secret of this invention to an artist named Waldech,
was careful to exclude all extraneous light ; and, to avoid any noise
produced by the apparatus, the wheels were covered with wool.
He further augmented the illusion by imitating the noise of thunder,
rain, the cries of animals, &c.

In Fig. 231, a double lantern is shown, from which, beside'
the image of the spectre or any other fantastic personage, that

304

PHYSICAL PHENOMENA.

[BOOK in.

of a landscape in harmony with the scene produced, can be projected
on the screen.

The same double apparatus also gives polyoramic views ; that
is, effects of varied landscapes, a succession of day and night, calm

sea and tempest, &c. Each lan-
tern is disposed in such a manner
as to project each double view at
the same place on the screen.
One of them is at first closed,
and a landscape illuminated by
the sun is seen ; by degrees the
light diminishes, twilight comes,
then night, and imperceptibly the
second view is substituted for
the first. Children and even
grown persons, often admire these
^pictures and effects of light :
the principle interests us here,
rather than the details of the
mechanism.

We shall only insist on this
point, viz. that the dark chamber,
megascopes, magic lanterns, and phantascopes are all based on the
formation of real images, by means of converging lenses.

Such is also the
principle of the
solar microscope,

fHUMlil JK^ which is not less

interesting than
the instruments
before described,
and certainly more
useful for the
study and teach-
ing of science.

The solar mi-
croscope is used to
project the image of a small object, in a considerably enlarged form,

FIG. 231.— Plmntascope.

FIG. 232. — Solar microscope ; complete.

CHAP. VI.]

REFRACTION OF LIGHT.

305

on a screen. It is a megascope with the advantage of easy use,
and of showing the enlarged object to a great number of spectators.
To this end, the object is placed a little beyond the principal focus
of a lens of short focus. The enlargement is more considerable as
the distance of the object from the focus decreases. But the image
will be formed at a much greater distance from the lens ; and, the
greater the magnifying power, the more will the light be diffused,
and consequently enfeebled ; hence the necessity of illuminating the
object as brightly as possible, so that the image may retain a
sufficient degree of distinctness. This is why either the rays of
the sun, or those of a very intense source of light, such as the electric
light, are used. A mirror reflects and projects the rays of light on

FIG. 233. — Section of the solar microscope.

a lens of large aperture, which causes them to converge for the first
time ; a second lens concentrates the rays still more ; and at the focus
the object, the details of which we desire to examine, is placed.
Figures 232 and 233 represent the solar microscope and its internal
construction. The gas microscope is that in which Drummond's light
is used to illuminate the object ; and the photo-electrical one that in
which the brilliant voltaic arc supplants the solar rays.

Nothing is more curious than to see the magnified images of
the various organs of the smallest animals ; the infusoria which live
in a drop of fermenting liquid ; the decomposition of water into
gaseous globules of oxygen and hydrogen ; the crystallization of
salts ; and the structure of animal and vegetable tissue.

30C . PHYSICAL PHENOMENA. [BOOK in.

CHAPTER VII.

COLOURS: THE COLOURS IN LIGHT SOURCES, AND IN NON- LUMINOUS
BODIES— DISPERSION OF COLOURED RAYS.

White colour of the sun's light — Decomposition of white light into seven simple
colours ; solar spectrum — Recomposition of white light by the mixture of the
coloured rays of the spectrum — Newton's experiment ; unequal refrangibility
of simple rays — Colours of non-luminous bodies.

THE light which physicists take as a type of all others as regards
colour is that of the sun. That the light of the sun is white
may be proved by a very simple experiment. If in the interior of a
dark room, tne solar light, after passing through a hole in the shutter,
is received directly on a piece of white paper, the image of the sun on
the paper will be found to be a round white spot. If this experiment
were not made in a dark room it would be inconclusive, because the
paper would receive, in addition to the solar rays, rays reflected from
the surface of other bodies differently coloured.

But this white light is not simple. It is composed of a multitude
of colours or tints, which are themselves simple colours. This has
been proved beyond doubt by a series of experiments which have
been made under diverse conditions, and which are principally due
to Newton. We will indicate the most striking of these.

If we place in the path of the solar rays, after their passage
through the round hole of the shutter of a dark room, a triangular flint-
glass prism in such a manner that its edges are placed horizontally
(Fig. 234), and that the beam enters it obliquely by one of its surfaces,
we shall see on the screen, at a certain distance abcrve the point where
the spot of light appeared before the interposition of the prism, a pro-
longed luminous band, formed of a series of extremely bright colours ;
this band is called the solar spectrum. The following is the order
in which the colours succeed each other when the prism has its base

CHAP, vii.] THE COLOURS IN SOURCES OF LIGHT. 307

upwards ; the order is the reverse when the base is turned down-
wards. At the lower extremity of the spectrum is a bright, full red,
to which succeeds an orange tint, and this passes by imperceptible
gradations into a magnificent straw-yellow. Then comes a green of
remarkable purity and intensity ; then a greenish blue tint ; and then
a decided blue colour, which becomes eventually indigo. After the
indigo succeeds violet ; the palest shade of which ends the spectrum.

Fio. 234. — Decomposition of light by the prism. Unequal refrangibility of the colours of the spectrum.

Plate II., Fig. 1, shows the series of colours of the solar spectrum
as obtained by a prism filled with bi-sulphide of carbon. Thus a ray
of white light is, as we have before stated, the reunion of a series of
coloured rays, of which we have mentioned only the principal ; for
the transition of one colour into another is made in such an imper-
ceptible manner, that there is no abrupt change of colour nor solu-
tion of continuity.1 Such is the phenomenon of the decomposition, or
analysis, of white light, which is also called the dispersion of the
coloured rays.

1 Except by the very fine black lines, of which we shall speak further on

308 PHYSICAL PHENOMENA. [BOOK in.

The dispersion of light by refraction is manifested to us every
day by numerous phenomena, some of which the ancients also ob-
served, but without suspecting the true cause. Precious stones, such
as diamonds, emit lights of different colours ; and the decomposi-
tion of light by one of its facets is not one of the least beauties of
this precious substance. The rainbow is a phenomenon due to the
same cause, as we shall show when we come to the description of
meteors. It is the same with the various colours which tint the clouds
and atmospheric strata at the time of the sunrise or sunset. Lastly,
in glass vessels containing transparent liquids, and in pieces of glass
cut as lustres, we see in certain directions iridescent fringes, presenting
the colours of the spectrum in all their purity.

A second experiment proves that each of the colours of the
spectrum is simple, and that the degree of refrangibility increases from
the red to the violet. This experiment consists in allowing a narrow
beam of the coloured light to pass through a small hole made in the
screen, at the point where the red light falls, for instance ; when this
is received on a second screen (Fig. 234), it forms a red image at a
point which is carefully noted. If, instead of receiving it directly on
this screen, a second prism is interposed, the luminous beam is again
deviated to a higher point than before. But the new image is red
like the first, and of the same form if the prism is properly placed >
therefore, the red light of the spectrum cannot be decomposed. The
same experiment, repeated with other colours, gives analogous results.
All the colours of the solar spectrum then are undecomposable or
simple ; but their refrangibility increases, for it is noticed that the
distances between the direct images of the colours on the screen and
the images obtained by refraction in the second prism are greater as
the colour is nearer the extreme violet of the spectrum.

If, instead of a prism formed of flint-glass, we use prisms of other
solid or liquid refractive substances, we obtain spectra more or less
brilliant, and more or less elongated; if the prisms are colourless,
the spectra are composod of the above colours, arranged in the same
order ; but their proportions — that is, the spaces occupied by each of
them — vary according to the nature of the substance, whilst the order
of the colours remains the same. Flint-glass, among solids, gives the
most extended spectrum, especially at the violet end, and bi-sulphide
of carbon among liquids.

CHAP. VII.]

THE COLOURS IN SOURCES OF LIGHT.

309

The angle of the prism also influences tha length of the spectrum
produced, which is greater as the angle is more obtuse. This fact may
be easily proved experimentally, by the aid of prisms having various
angles, of which we have spoken above. Thus, white light is decom-
posed by refraction into rays differently coloured, and the colour of
each of the rays corresponds to a particular degree of refrangibility.

This is the analysis of light.

But, if such is indeed the composition of light, white light ought
to be produced by uniting all the colours of the spectrum in proper
proportions.

Various experiments confirm this consequence of the analysis

FIG. 235.— Recompoaition of light by a lens.

of light. Most of them are due to Newton, who described them
in his " Optics," and they are reproduced in the present day with
very slight modifications. The most simple experiment of this
nature consists in receiving on a converging lens the solar spectrum
produced by a prism. On placing a screen of white paper at the
focus where the rays of the different colours are brought to a point (it
is the conjugate focus of the point whence the rays emerge from the
prism) a white image of the sun is- seen (Fig. 235). By bringing the
screen nearer to the lens, the separated coloured rays again reappear,
brighter as the screen is gradually brought nearer the lens. On the
other hand, if the screen is moved away from the lens, starting from the

310 PHYSICAL PHENOMENA. [BOOK in.

point of convergence, the colours again appear, so that the red, for-
merly at the bottom, is now at the top ; and the violet, which was at
the top, now occupies the lower portion of the coloured band. By
using two prisms of the same substance and angle, but placed in
reverse positions, as in Fig. 236, the beam of white light which falls
on the first prism is divided into differently coloured divergent rays ;
but refraction brings them to parallelism on their emergence from
the second prism, and, instead of a spectrum, a beam of white light,
produced by the reunion of the differently coloured rays, is seen.
But the upper edge of the image received on the screen is red, and
the lower one violet ; because, among all the rays of white light

forming the beam, the
mean rays alone give rise
to spectra the colours
of which reunite, while
the extreme rays of the
spectrum are not super-
posed on any other colour,
and recomposition can-
not be effected at these
points.

Two spectra obtained

Fio. 236.-Recomposition of light by prisms. by meang Qf fcwQ different

prisms and projected in inverse directions on a screen give white
light at the place where the colours are superposed.

If the spectrum given by one prism is observed with a second
prism, a position may be found in which the image received by the
eye is round and white.

All of these experiments, and others also, are described by .Newton
with admirable clearness and simplicity. " Hitherto," he sa,ys, " I
have produced white by mixing the colours produced by prisms.
Now, in order to mix the colours of natural bodies, take water slightly
thickened by means of soap, and agitate it until it becomes frothy.
When this froth has come to a state of rest, if you examine it
attentively, you will see various colours on the surface of each
bubble of which the froth consists. But if you remove to such a
distance that you cannot distinguish the various colours, the froth
will appear perfectly white." (" Optics," Book I.)

CHAP. V1T.]

THE COLOURS IN SOURCES OF LIGHT.

311

He also tried to obtain a white tint by the mixture of certain
proportions of various coloured powders. Orpiment (orange-yellow
sulphide of arsenic) mixed with purple, green, brown, and blue,
gave him a composition of an ash-coloured grey, which, when exposed
to sunlight and compared with a piece of white paper of the same
size placed by the side of the mixture and in the shade, appeared of
a brilliant white. Newton explains the grey colour of mixtures of
this kind by the absorption of light, and it was to obviate this
diminution of brightness that he thought it better to illuminate the
composition strongly by the solar rays.

Lastly, if a disc, divided into sectors coloured with the prin-
cipal colours of the
spectrum, is caused to
revolve rapidly, in pro-
portion as the rotation
increases, the indi-
vidual colours disap-
pear from the eye.

The disc ultimately
assumes a tint which
approximates to white
according as the true
proportion of the dif-
ferent colours has been
the better observed.
It will be understood
that when the succes-
sive impressions of the

different colours on the retina are confused, in consequence of the
rapidity of the movement, it is as if the rays made their impres-
sion simultaneously, and the sensation which is produced is that
of white. The same experiment can be very simply shown by
spinning a top, the surface of which is divided into sectors, in the
direction of meridional lines, and painted with the colours of the
spectrum. This will appear white or a greyish-white in proportion
as its rotation is the more rapid, and the colours will gradually
reappear as the motion slackens.

The phenomena which we have just described are produced

FIG. 237.— Recomposition of white light by a revolving disc.

312 PHYSICAL PHENOMENA. [BOOK in.

by solar light. But it must not be forgotten that by this term
must be understood not only the light due to the rays which arrive
directly from the sun, but also all light originating from this body .
that of clouds, the atmosphere, and the light of the moon and planets.
Analysed by means of a prism, these give spectra of very variable
brightness, but their composition as regards coloured rays is precisely
the same as that of the solar spectrum.

FIG. 238.— Unequal refrangibility of various colours.

Lights proceeding from other sources, stars, artificial flames, the
passage of electricity, either in physical apparatus or in storms, all
produce spectra, in which the colours are disposed in the same order
as the colours of the solar spectrum. But generally speaking the
phenomenon is less brilliant, and, as we shall soon see, it happens
in some cases that certain colours are not seen, and are found to be
replaced by dark lines.

CHAP. VII.]

THE COLOURS IN SOURCES OF LIGHT.

313

The experiments which serve to show that the different colours
of the spectrum give, by their reunion, white light, are as conclusive
when we use the coloured rays of the spectrum, as when the colours
of illuminated bodies are employed. This is in itself sufficient to
prove that these latter colours are, like those of luminous sources,
unequally refrangible. But Newton made direct experiments on this
difference by examining with a prism a piece of paper, the two halves
of which were differently coloured, the one being red, the other
blue. The prism and the paper were placed in front of a window, as
shown in Fig. 238, and he noticed that the two halves of the paper
appeared unequally deviated, the blue half being lower than the red,
so that the paper appeared divided into two parts, the one . no longer
a continuation of the other; the reverse happened when the angle
of the prism was placed in the contrary direction ; therefore blue is
more refrangible than red.

FIG. 239.— Unequal refrangibilities of simple colours. Newton's experiment.

By receiving on a screen of white paper placed behind a lens
the images of the same paper illuminated by a candle, Newton like-
wise discovered that the screen must be placed at different distances
to obtain clear images of the blue half and the red.

A black silk cord which was twisted round the paper enabled
him to determine with greater facility the place where the image of
each colour was formed with distinctness, for, in other places, the
images of the threads were confused. For the blue half the distance
of the image to the lens was less than in the case of the red half,
which again proves that the blue is more refrangible than the red.
These two experiments are the first described by Newton in his
" Optics."

That which we call the natural colour of a body is the colour

B B

314 PHYSICAL PHENOMENA. [BOOK in.

which is presented to us when it is illuminated by a very pure white
light, as by sunlight. If its surface has the property of absorbing all
the coloured rays of the spectrum with the exception of one, red for
example, the body appears to us red, because it only reflects to our
eye the red rays of the spectrum. If this surface absorbs but a limited
number of coloured rays, the colour of the body will be that which
proceeds from the mixture of the non-absorbed rays ; and this
explains the considerable number of colours and shades of bodies,
which indeed are much more varied that those of which the
spectrum itself is composed.

That substance which is able to reflect in an equal proportion all
the colours which compose white light, is itself white, and it is
brighter according as this proportion is greater. On the other hand, as
this proportion diminishes, the white colour diminishes in intensity,
and becomes a deeper and deeper grey, lastly attaining black, when the
absorption of all the coloured rays of the spectrum is as complete as
possible. Black bodies are therefore those whose molecular constitu-
tion is such, that all the rays which constitute white light are
absorbed by their surface ; whilst white bodies are those which reflect
them all, and coloured bodies are those which reflect certain rays and
absorb others. If this explanation is true, it is susceptible of many
experimental verifications.

Let us take a white body and arrange it so that it only receives
the yellow rays of the spectrum. This is easily done by placing it
in a dark chamber, and admitting only the yellow rays of the spec-
trum obtained by means of a prism. The body will appear yellow.
It would be red, green, blue, &c., if it were lighted up by red, green, or
blue rays. On the contrary, a black body will remain black whatever
the colour by which it is illuminated. Lastly, a red body will appear
of a deep red, if it is lighted up with the light proceeding from the
red rays of the spectrum, whilst it will appear black if we expose it
to the rays of other colours.

Experiment confirms these results. It is observed, however, that
coloured bodies take the tint of the rays which illuminate them, even
when these rays are not of the colour of these bodies ; and that this
tint is much brighter where there is greater analogy between their
own colour and that of the rays with which they are illuminated.
Thus " vermilion placed in red appears of a most brilliant red ; in

CHAP, vii.] THE COLOURS IN SOURCES OF LIGHT. 315

the orange and yellow, it seems an orange and yellow, but its bright-
ness is less. The green rays also give it their colour, but, on account
of the great inaptitude of the red to reflect the green light, it appears
dark and dull ; it becomes still more so in the blue, and, in indigo and
violet, it is nearly black. On the other hand, a piece of dark blue or
Prussian blue paper takes an extraordinary brilliancy when exposed
to the indigo rays. In green it becomes green, but not very bright ;
in red, it appears nearly black." (Sir John Herschel.)

Newton's theory must therefore be thus understood : that the sur-
faces of coloured bodies are generally apt to reflect the rays of a
certain colour in a much greater quantity than those of other rays ;
and that gives them their predominant colour. These surfaces, never-
theless, do not entirely absorb the other rays, and that prevents them
from being perfectly black when they are illuminated by coloured
lights different from those which they generally reflect.

The colours of bodies are seldom identical with those composing
the solar spectrum, as they are principally composite ; evidence
of which can be obtained by submitting them singly to analysis by
the prism. This analysis gives a spectrum formed of various simple
colours, the mixture producing the particular colour observed. It is
sufficient to look at a coloured object, as a flower or a piece of dyed
stuff, through a prism, to see that the edges of the image, parallel to
the edge of the prism, are banded like the rainbow.

If, instead of illuminating a coloured body by the white light of
the sun, or by one or other of the simple colours of which this
light is composed, we use other luminous sources, such as the light of
a lamp or artificial flames, the colour is found to be altered. Thus
we all know that green appears blue by the light of a lamp. But
let us first finish what we have to say of Newton's theory concerning
the colours of non-luminous bodies.

In endeavouring to penetrate more deeply into the causes of this
phenomenon, Newton supposed that the incident light is decomposed
at the surface ; one part is absorbed, — extinguished in opaque bodies
and transmitted in transparent ones ; the other part is reflected by the
superficial molecules, — at a very little depth in opaque bodies, and at
any depth in transparent ones. This explains why, in the latter, the
colour of transmitted light is generally different from that of reflected
light. For example, we have seen that gold reduced to extremely

B B 2

316 PHYSICAL PHENOMENA. [BOOK in.

thin leaves allows a greenish blue light to pass through it, while its
reflected colour is yellow, or reddish yellow. " Halley, having
descended to a depth of several fathoms in a diving bell, saw that the
upper part of his hand, on which fell the solar rays after passing
through a glazed opening, was of a crimson colour ; the under part,
which was illuminated by light reflected from deep water, appeared
green; whence Newton concluded that water allowed the red rays
to pass through it and reflect the violet and blue." (Daguin.)

We must distinguish between light reflected regularly, or specu-
larly, and that diffused light which is scattered from the surfaces of
bodies. The first has nothing to do with the colour of bodies ; and
indeed we know that perfectly polished bodies represent the images
of the bodies they reflect, coloured like the bodies themselves; while
their own colour remains unperceived.

To what modification is light which is diffusely reflected sub-
mitted ? How does the structure of bodies act on the different
coloured rays, so as to reflect some and extinguish others ? Is it the
form, density, refractive power of the molecules, or, rather, is it these
united elements which give place to the phenomenon of various
colorations? These are excessively subtle questions, which cannot
be answered with exactitude in the present condition of science.

CHAP, viii.] COLOURS. 317

CHAPTER VIII.

COLOURS.

Classification of colours- — Tones and scale of the colours of the solar spectrum, after
the method of M. Chevreul — Chromatic circles of pure and subdued colours ;
tones and scales— Complementary colours.

THE white light of the sun, decomposed by means of a prism,
produces a series of colours which correspond, as we have
seen, to different degrees of refrangibility. These colours are, so to
speak, infinite in number, as they pass from one end of the
spectrum to the other by imperceptible shades; but it is customary
to distinguish seven principal colours, the names of which, taken
in their natural order, form a crude Alexandrian verse :
Violet, indigo, blue, green, yellow, orange and red.

Some physicists, believing in the possibility of reproducing some
of these colours by the mixture of others, — green, for example, being
obtained by the juxtaposition of yellow and blue, violet by that of
blue and red, and so on, — have endeavoured to prove that the spec-
trum is only formed of three elementary colours. According to
Brewster these colours would be red, yellow, and blue ; according to
Young, red, green, and violet. The proportions in which they are
mixed in the different parts of the spectrum would account for the
variety of shades of which ifc is composed. In the present day, these
theories are rejected ; the experiments by which they were supported
having been proved to be inexact. All the colours of the spectrum
are therefore simple colours, the number of which can be considered
as infinite ; although, in practice, they are reduced to seven principal
colours.

White is not a simple colour, but, on the contrary, the most
complex of the composite colours. Black is not a colour; it is

318 PHYSICAL PHENOMENA. [BOOK m.

the complete absence of all light. As to the composite colours
which natural bodies present to us, they are due to combinations,
in various proportions, of all the elementary colours.

A very simple experiment proves that the combination of all the
rays of the spectrum is necessary to produce perfect light. It consists
in intercepting a certain portion of the spectrum before it falls on
the lens which is used for the recomposition of the light. Thus,
if the violet be intercepted, the white will acquire a tinge of
yellow ; if the blue and green be successively stopped, this yellow
tinge will grow more and more ruddy, and pass through scarlet
to orange and blood-red. If, on the other hand, the red end of the
spectrum be stopped and more and more of the less refrangible por-
tion thus successively abstracted from the beam, the white will pass
first into pale, and then to vivid green, blue-green, blue, and finally
into violet. If the middle portion of the spectrum be intercepted,
the remaining rays, concentrated, produce "various shades of purple,
crimson, or plum-colour, according to the portion by which it is
thus rendered deficient from white light ; and, by varying the
intercepted rays, any variety of colours may be produced ; nor is
there any shade of colour in nature which may not thus le exactly
imitated with a brilliancy and richness surpassing that of any
artificial colouring.

The number of composite colours, obtained by the combination
of simple colours, or the different coloured rays of the spectrum,
increases to an almost indefinite amount. But we shall presently
see that it is possible to increase them still more, either by the
addition of a certain quantity of white light, or by the mixture
of black in various proportions.

Two colours which, by their combination, produce white are
called complementary colours.

There is a very simple method of determining the groups of
colours which possess this property : it consists in the interception,
as it issues from a lens, of a portion of the convergent beam
about to meet at the focus. This portion received on a second
prism will be deviated, and will give a colour which will be evidently
complementary to the colour produced at the focus of the lens, as
before their separation they formed white.

Helmholtz discovered, by a different process, which consisted in

CHAP, viii.] COLOURS. 319

receiving the spectrum colours through slits in a screen and then
concentrating them by a lens, that there is an indefinite number
of groups of two colours susceptible of forming, by their mixture,
perfect white. The following are some of the results obtained by
that physicist : —

Complementary Colours. Intensities of the two Colours.

Violet — greenish yellow ..... 1 — 10

Indigo — yellow 1 — 4

Blue — orange 1 — 1

Greenish blue — red 1 — 0'44

The numbers which follow these groups measure the relative in-
tensities of each of the colours and refer to a bright light;
they vary when the incident light itself varies in intensity.
Helmholtz has devised an extremely simple method of studying
the resultant of the mixture of two colours, which are placed
on two adjacent discs. When an unsilvered glass is placed
vertically between them, one of the discs is seen directly ; the
other through the transparent plate. Moreover, the first is seen a
second time, by reflection. If it is then placed in such a position
that its image appears superposed upon the disc seen through
the glass, the two colours will be found naturally blended, and
one can easily judge of the shade produced by their composition.
Thus, also, two discs, coloured, the one by chrome yellow, the
other by cobalt blue, produce pure white ; which proves that these
colours are complementary.

To sum up, a simple or composite colour always has its comple-
mentary colour ; moreover, it has an infinity of them, for if to the
complementary colour we add white light in variable proportions,
the resultant can only be white. But this rule can only be
applied to clear colours, that is to say, those which are not altered
by any proportion of black ; in this case, instead of perfect white,
a grey or greyish- white would be obtained.

Lastly, the mixture of complementary colours only produces
white when it is not a material mixture ; if material colours are used,
moistened in whatever way, or even in a pulverulent state, the
mixture will only give a more or less decided grey. If the colours,
whether simple or composite, are indefinite in number ; if the mix-
ture in different proportions of white or black again multiplies that

320 PHYSICAL PHENOMENA. [BOOK in.

number ; it is no less true that the eye can only appreciate a limited
quantity. Yet, if it were possible to collect in one scale all the
shades of colours presented to us by Nature, arid to distinguish
them from each other, we should be astonished at the richness and
magnificence of that palette. The leaves and flowers of plants,
the skins of animals, the brilliant colours which the feathers of
birds possess, the wings of butterflies and other insects, shades
of different minerals and shells, would furnish elements of the
innumerable series of natural colours, and would pass from one
shade to another by imperceptible gradations. Thus we could
have a classification of colours derived from natural objects.

Colours used in the arts are probably much more restricted ; we
can nevertheless form an idea of their number by this fact — that
the Komans used, it. is said, more than 30,000 tints in their mosaics.

But even this number, precisely because it is considerable, causes
the want to be felt of a proper classification of colours and their
shades, which would enable them to be defined by showing their
relationship to a fixed type, determined once for all. We all know
that, in industries and the arts, the nomenclature of colours is
very arbitrary or, at least, varies in one art or industry from another :
the names are borrowed from natural objects, minerals, flowers,
fruits, and animals, but there is no line of gradation between them.
In order to obviate the inconveniences resulting from this confusion,
M. Chevreul, celebrated for his chemical labours and his study of
colours, proposed a classification of colours and their shades. The
principles and basis of this we will now describe.

According to M. Chevreul, a substance possessing any one of the
colours of the spectrum can only be modified in four different ways :

1. By white, which reduces it in intensity.

2. By "black, which diminishes its specific intensity.

3. By a certain colour, which changes the specific property with-
out rendering it less bright.

4. By a certain colour which changes the specific property
and renders it less bright, so that if the effect is carried to the
highest degree, it results in black or normal grey, represented by
black mixed with white in a certain proportion.

To express all these modifications, M. Chevreul uses the following-
expressions, which once defined can no longer be equivocal : —

CHAP, viii.] COLOURS. 321

He calls the tones of a colour the different degrees of intensity
of which this colour is susceptible, according as the matter which
presents it is pure or simply mixed with white or black ; the scale,
the whole of the tones of the same colour ; the shades of a colour,
the modifications which it undergoes by the addition of another
colour which changes it without rendering it less bright ; lastly,
the subdued scale, the scale whose light tones as well as the dark
ones are tarnished with black. M. Chevreul obtained a scale
sufficiently extensive for the principal colours and their tones and
shades by the following means : —

Having divided a circle into seventy-two equal sections, he placed,
at equal distances, three patterns of tinted wool, one red, another
yellow, the third blue ; as fresh and pure as possible, and of the
same intensity of colour. Between these three sections, and at
an equal distance from each, he placed orange between the red and
yellow, green between this latter and the blue, and violet between
the blue and red. By continuing in the same manner succesive
intercalations of intermediate colours and shades, he at last ob-
tained what he called a chromatic circle of fresh colours, so as to
reproduce the spectrum of solar light.

When these seventy-two shades were obtained, he took each
of them to make a complete scale formed by the addition of
increasing quantities of white and black, in order to have ten sub-
dued tones and ten tones of the same colour rendered clearer by white.
Each scale therefore comprised, from pure white to pure black,
which were the extremities, twenty different tones, of which the
pure colour is the tenth, starting from white.1

From, this first combination there are already 1,440 different
tones, all deduced from the chromatic scale of pure colours : but
in successively subduing the seventy-two tones of this circle by
the addition of 1, 2, 3, &c. tenths of black, nine circles of subdued
colours are formed ; and each of the seventy-two tones which
they comprise becoming in its turn the type of a scale of twenty
new ones proceeding from white to black, there follows, for the
complete series, a scale of 14,400 tones, to which must be again

1 " Des Couleurs et de leurs Applications aux Arts industriels d 1'aide desCercles
chromatiques." The text of this work is accompanied by twenty-seven steel
engravings, coloured by Eene Digeon.

0 C

322 PHYSICAL PHENOMENA. [BOOK in.

added the twenty tones of normal grey, which make 14,420
different tones.

It is evident that such an extensive scale ought to suffice for
most of the scientific and industrial applications, and will most
frequently exceed the wants of artists. Unfortunately, the rigo-
rously exact material reproduction of all these colours is of great
difficulty, and it is no less difficult to preserve the types when
once they are obtained. The chromatic construction of M. Chevreul
must be reproduced in unalterable colours, — for instance, in pictures
enamelled on porcelain. Scientific research would not be less
interested than the arts to possess fixed types, to which the colours
of natural objects, so often changed by time, would be brought
back again by the help of the order of numbers, and thus made
easy of reproduction. M. Eadde has recently patented a colour
gauge, with about 10,000 shades of colour, and he claims for it: —

1. That he can reproduce the colours in it with absolute
accuracy.

2. That as the colouring material is worked into the texture
of the substance in which it appears, it is indestructible and
unalterable.

CHAP, ix.] LINES OF THE SOLAR SPECTRUM. 323

CHAPTER IX.

LINES OF THE SOLAR SPECTRUM.

The discoveries of Wollaston and Fraunhofer ; dark lines distributed through the
different parts of the solar spectrum — Spectral lines of other luminous sources
— Spectrum analysis ; spectrum of metals ; inversion of the spectra of flames
— Chemical analysis of the atmosphere of the sun, of the light of stars, nebulas?
and comets.

"VTEWTON", in studying the different parts of the solar spectrum,
-L^ by means first of circular and afterwards of elongated apertures,
could not distinguish any indication of the precise limits of its
various colours : they appeared to blend witli" one another in an
imperceptible manner and without interruption. He was persuaded^
however, by his experiments, that the coloured rays which constitute
white light possess, from the extreme red to the extreme violet,
all possible degrees of refrangibility, and he regarded each of these
rays as simple and homogeneous, imagining that the light de-
composed by the prism was spread out in' a continuous manner
throughout the whole spectrum.

It is curious that Newton did not go further — that he did not
reduce the aperture to a fine line of light, in which case the colours
would have been seen in all their purity, and would not have been
mixed and confused by the overlapping of each colour on its
neighbour.

This step in advance was reserved for the beginning of the present
century, and then a great discovery was made. It was found that
here and there in the different colours there were gaps in the light ;
in other words, that there were dark lines in the sun's spectrum.
This was first detected by Wollaston in 1802, but the discovery was
independently made and largely elaborated by Fraunhofer.

C o 2

324 PHYSICAL PHENOMENA. [BOOK in.

Joseph Fraunhofer, who was born in 1787, at Straubing, a little
town in Bavaria, was the son of a glazier. He was at first a worker
in glass, but, by labour and perseverance, he succeeded in meriting the
reputation of being the most ingenious and learned optician of our
century. Fraunhofer was not satisfied with bringing the con-
struction of optical instruments to a perfection then unknown ;
but, being a consummate observer, he employed the instruments
which he manufactured, to make various discoveries, amongst which,
that to which we have referred is one of the most curious and
most fruitful in its results.

In the attempt to measure the refractive indices of the coloured
rays, and to find particular points in the spectrum capable of being
used as marks, Fraunhofer discovered the great fact, that the light
of the solar spectrum is not continuous, but that it is divided by
a multitude of fine black lines, which form so many sharp inter-
ruptions in the luminous band.

In this experiment, which requires the most delicate manipula-
tion, he made use of a prism of pure flint-glass, free from striae,
upon which a beam of sunlight, which had previously passed
through a very fine slit parallel to the edge of the prism, was caused
to fall. The spectrum thus obtained, when observed by means of a
magnifying glass, showed him, instead of a continuous band in which
the colours blended into each other without interruption, a ribbon
crossed in the direction of its width, with numerous dark and black
lines very unequally spread over the spectrum. The distribution of
these lines did not appear to have any relation to the tints of the
principal colours.

Fraunhofer varied this experiment in a variety of ways ; but,
as long as the luminous source was sunlight, either direct or re-
flected, the same dark lines always appeared, and they preserved the
same relations of order and intensity. If, instead of a flint-glass
prism, a prism of any other substance, liquid or solid, be employed,
the distances between the lines vary, but otherwise they always
occupy the same positions relative to the colours of the spectrum.

The illustrious optician of Munich studied this remarkable
phenomenon with infinite care : he determined, with great precision,
the positions of 580 dark lines, and, for use as marks and com-
parison, he distinguished among this number eight principal lines,

CHAP. IX.]

LINES OF THE SOLAR SPECTRUM.

325

which he called by
the first letters of the
alphabet. The solar
spectrum of Plate II.
shows the position of
these lines, as they
were obtained with
a prism filled with
bisulphide of carbon.
The lines A, B, c,
are all found in the
red, the first at the
extremity of the spec-
trum, the second at
the middle of the red,
and the third at a
little distance from
the orange. The
double line D forms
nearly the limit of the
orange near thegreen ;
E in the middle of this
last colour ; F at the
middle of the blue ;
G and the double line
H are, one at the end
of the indigo towards
the blue, the other at
the end of the violet.
Since 1817, when
Fraunhofer observed
the lines which bear
his name, new dark
lines have been no-
ticed, and, at the pre-
sent day, more than
2,000 have been
mapped by Kirch-
hoff and Angstrom.

FIG. 240.— A fragment of the solar spectrum.

326 PHYSICAL PHENOMENA. [BOOK m.

The more recent researches of Rutherford and Lockyer have in-
creased the number of the definitions indefinitely.

We obtain some idea of this multitude of lines in examining
Fig. 240, which reproduces a portion of the solar spectrum, com-
prised between the principal lines D and E. Sir David Brewster, who
was much occupied in these researches, in addition to the usual precau-
tions indispensable in obtaining a clear and pure spectrum, increased
the sensibility of his sight by using ammonia gas, the dissolving
action of which destroyed the fluid veil which covers the surface
of the eye.

Fraunhofer did not confine himself to the study of the lines which
break the continuity of light in the solar spectrum ; he also applied
his beautiful method of observation to the spectra of other sources of
light. And at first, as was to be supposed, he found the same lines in
the bodies which reflected solar light to us, such as clouds or pure
sky, moon and planets : the lines were the same, but they possessed
less intensity. By observing the spectrum of the brightest star,
Sirius for example, he found it also crossed by dark lines : but much
less numerous and not distributed in the same manner as in the
solar spectrum; moreover, he discovered that the lines varied in
the various stars. Lastly, he applied the same method of observa-
tion to the electric light; and, instead of dark lines, he saw in
this spectrum a certain number of bright lines.

Such are the celebrated experiments which served as starting
points to a series of brilliant discoveries, the whole of which now
constitute one of the most important branches of optics, and aid
chemistry by the most ingenious and delicate method of analysis.
We will now endeavour to give some idea of this method, known
as spectrum analysis.

Solar and stellar spectra are, as we have seen, striped with dark
lines which indicate interruptions in the emission of light, and
prove, contrary to what was at first believed, that in the light
proceeding from these light sources there are not rays which possess
every possible degree of refrangibility. The contrary effect takes
place in the spectra of all incandescent bodies, either in the solid,
liquid, or densely gaseous condition : the spectra of these lights are
continuous : there are no breaks in the spectrum.

Vapours and gases, however, which are not dense give different
results. If we introduce into an artificial flame, such as a jet of gas

CHAP. IX.]

LINES OF THE SOLAR SPECTRUM.

327

or a spirit-lamp, certain metallic substances, which the high tempera-
ture of the source can convert into vapour, continuous spectra are no
longer observed, but bright lines separated by wide, comparatively
dark, intervals : Fraunhofer had already remarked this. Gases also,
rendered incandescent by the electric spark, give similar spectra.

Since his time, the fact has been studied in all its phases and
by various methods. It has been discovered that the bright lines
of metallic vapours, and gases when not very dense, vary, in number

FIG. 241.— Spectroscope.

and position, according to the metal or gas ; and the spectra change
as the pressure of the gas is altered.

To study spectra of this kind, physicists employ instruments
called spectroscopes. Fig. 241 represents one of these. The flame
of a gas-lamp is placed in the axis of a lens to which light pene-
trates through a narrow slit ; the slit and lens forming what is
called the collimator. The slit being in the focus of the lens, the
light passes through the prism in a parallel beam. The light which

328 PHYSICAL PHENOMENA. [BOOK in.

passes through the refractive medium is made to form an image of
the slit at the focus of another lens, which image is examined by
an eyepiece. This arrangement, which is a great improvement upon
that adopted by Fraunhofer, is due to an English optician of great
celebrity, Mr. Simms.

To obtain the spectrum of the vapour of a metal, for instance that
of sodium, we introduce into the flame of a lamp a platinum wire,
impregnated with a concentrated solution of salt, of which this
metal forms the base, sea-salt (chloride of sodium) for instance.
We soon perceive a yellow ray of great intensity and sharp out-
line. This is the only line of the sodium spectrum. (Plate II.)

The vapour of lithium gives two principal lines, one a pale yellow,
the other red and bright; potassium gives two characteristic lines,
red and violet, accompanied by yellow and green lines ; calcium
gives a very bright green line, one orange, and one blue ; strontium
gives eight lines, six of which are red, one orange and one blue ;
barium, two green lines ; thallium, one green line, remarkable for its
brilliancy.

The vapours of a great number of simple bodies have thus been
studied, the bright lines of their spectra discovered, and their position
fixed. No two vapours or gases have the same spectrum. Hence
results a new method of analysis, which is so delicate that a millionth
part of a milligramme of sodium is sufficient to show immediately
the characteristic yellow ray of the spectrum of this metal. Two
German chemists and physicists, MM. Kirchhoff and Bunsen, were
the first to bring spectrum analysis to a high degree of precision.
" I take," says M. Bunsen, " a mixture of the chlorides of alkaline
metals and earths, — sodium, potassium, lithium, barium, strontium,
and calcium, — containing at most a hundred thousandth of a milli-
gramme of each of these substances ; I place this mixture in the
flame and observe the result. At first, the intense yellow line of
the sodium appears on a background of a continuous very pale
spectrum ; when it begins to be less sensible and the sea salt is
volatilized, the pale lines of the potassium appear ; they are
followed by the red line of the lithium, which soon disappears,
whilst the green rays of the barium appear in all their intensity.
The salts of sodium, potassium, lithium, and barium are therefore
entirely volatilized ; a few instants after, the calcium and strontium

CHAP ix.] LINES OF THE SOLAR SPECTRUM. 329

lines come out, as if a veil has been removed, and gradually attain
their form and characteristic brilliancy.

By the help of spectrum analysis, the presence of sodium' has • -
been, determined in the air and the dust floating about in a room/
The sensibility of the reaction of this metal is so great, that spectro-
scopic observers are obliged to take all kinds of precautions to
prevent the appearance of the sodium line ; even if we dust a book
near the instrument, the yellow sodium line immediately appears.

Five new metals have been discovered by this method : the
two first, csesium and rubidium, by MM. Bun sen and Kirchhoff ; the
third, thallium, by Mr. Crookes and M. Lamy ; the fourth, indium, by
MM. Eeich and Eichter; the fifth, gallium, so recently that it is
difficult to say to what family of elements it belongs. Prof. Odling's
discourse at the meeting of the British Association at Plymouth in
1877, contains the latest information with reference to it. The name
caesium is given from the two blue lines in its spectrum ; rubidium
from the red lines which characterize the spectrum of this metal;
the name thallium recalls a beautiful green line, and that of indium
a blue line near the indigo.

In these various lines then we have the power of detecting
the gases and the vapours of the various elements ; but this is not all
Eecent researches undertaken by Frankland and Lockyer have shown
that certain spectra undergo great changes by varying the pressure,
and that some lines in various spectra widen out, and become diffused
from increase of pressure, which also, when long continued, changes
-a typical gaseous spectrum — hydrogen, for instance — into a perfectly
continuous one, similar to those of solids or liquids.

Erankland and Lockyer have also shown that the various spectra
produced by varying the pressure can be, to a certain extent, repro-
duced by varying the quantity of any given vapour in a mixture.
Such researches as these give us ground for hoping that in time
this method of analysis may be employed quantitatively as well as
qualitatively, and explain Bunsen's experiment to which we have
before referred.

But we do not confine the power of the spectroscope to terres-
trial matter ; it has gone further : problems can be investigated and
solved by its means which had appeared inaccessible to human in-
vestigations ; the study of the chemical composition of the heavenly

330 PHYSICAL PHENOMENA. [BOOK in.

bodies, that of the sun and stars — these suns so prodigiously distant
from us ; of nebulae, which telescopes show us plunged in the abysses
of the ether at such distances that the imagination can scarcely
fathom the depth, and of comets.

Let us show in a few words how this has been done.

If we place a jet of gas before the slit of a spectroscope, and
lessen it so that it is scarcely perceptible, and burns with a bluish
flame, we observe that, in this condition, it will give no spectrum ;
there is complete darkness behind the prism. But, if a metallic
salt is introduced into the flame, sea-salt for instance, the yellow
ray of the sodium immediately appears, as we have just seen. If,
at the same time, and in the same instrument, we introduce a
solar ray in such a manner that the sodium spectrum and the
solar spectrum are superposed, a perfect coincidence will be noticed
in the position of the sodium yellow ray, and Fraunhofer's double
dark line D.

Now, for the sunlight let us substitute the intense light known
as Drummond's light — obtained by heating a piece of lime in a gas
burner into which a current of oxygen gas is introduced. The spec-
trum of this light, seen alone, shows a bright spectrum of perfect
continuity ; that is, containing none of the dark lines of the solar
spectrum. But if we interpose between the Drummond's light and
the slit of the spectroscope a sodium flame, the yellow sodium line
now gives place to a black line occupying precisely the same posi-
tion as the bright line did when the brighter light source was not
behind it.

It is this phenomenon which M. Kirchhoff calls the "inversion
of the spectra of flames."

It has been proved in regard to a great number of metallic
spectra. " If we cause," he says, " a solar ray to pass through a
flame of lithium, we see in the spectrum, in place of the usual red
line, a dark line, which rivals by its sharpness the most characteristic
of Fraunhofer's lines, and which disappears on removing the lithium.
The reversal of the bright lines of other metals is not so easily
effected ; nevertheless, M. Bunsen and myself have been fortunate
enough to invert the brightest lines of potassium, strontium, calcium,
and barium. . . ."

Now, what inference is to be drawn from this singular fact ? It

CHAP, ix.] LINES OF THE SOLAR SPECTRUM. 331

is that metallic vapours, endowed with the property of abundantly
emitting certain coloured rays, in preference to others, absorb
these same rays when they emanate from a more intensely luminous
source and traverse them. Thus, sodium light, which emits yellow
rays, absorbs the yellow rays of Drummond's light on their passage
through it. Hence results the black line, which occupies the same
position in the continuous spectrum which the bright sodium line
previously held.

If this absorption is a general fact, it must be concluded that
the black lines observed in the solar spectrum indicate the reversal of
as many bright lines by metallic vapours in the atmosphere of the sun.
This atmosphere, to us, acts the part of the sodium flame, and the
bright light of the sun's body that of the Drummond's light in the
same experiment.

This magnificent discovery, which has at one bound enabled us
to become familiar with the constituents of the atmospheres of all
the stars of heaven which are bright enough to show a spectrum,
is generally accorded to Kirchhoff and Bunsen, but the credit of it
is really due to an Englishman, Professor Stokes, who taught it as
early as 1852, while Kirchhoff and Bunsen did not announce their
discovery till 1859.

The observational and experimental foundations on which Pro-
fessor Stokes rested his teaching were as follows : 1 —

(1) The discovery by Fraunhofer of a coincidence between his
double dark line D of the solar spectrum and a double bright line
which he observed in the spectra of ordinary artificial flames.

(2) A very rigorous experimental test of this coincidence by
Professor W. H. Miller, which showed it to be accurate to an
astonishing degree of minuteness.

(3) The fact that the yellow light given out when salt is thrown
on burning spirit consists almost solely of the two nearly identical
qualities which constitute that double bright line.

(4) Observations made by Stokes himself, which showed the bright
line D to be absent in a candle-flame when the wick was snuffed
clean so as not to project into the luminous envelope, and from an
alcohol flame when the spirit was burned in a watch-glass. And

1 See Sir W. Thomson's Address as President of the British Association
in 1871.

332 PHYSICAL PHENOMENA. [BOOK m.

(5) Foucault's admirable discovery (EInstitut, Feb. 7, 1849), that
the voltaic arc between charcoal points is " a medium which emits
the rays D 'on its own account, and at the same time absorbs them
when they come from another quarter."

The conclusions, theoretical and practical, which Professor Stokes
taught, and which Professor Thomson gave regularly afterwards in
his public lectures in the University of Glasgow, were : —

(1) That the double line D, whether bright or dark, is due to
vapour of sodium.

(2) That the ultimate atom of sodium is susceptible of regular
elastic vibrations, like those of a tuning-fork, or of stringed musical
instruments; that, like an instrument with two strings tuned to
approximate unison, or an approximately circular elastic disk, it has
two fundamental notes or vibrations of approximately equal pitch ;
and tbat the periods of these vibrations are precisely the periods
of the two slightly different yellow lights constituting the double
bright line D.

(3) That when vapour of sodium is at a high enough temperature
to become itself a source of light, each atom executes these two
fundamental vibrations simultaneously ; and that therefore the light
proceeding from it is of the two qualities constituting the double
bright line D.

(4) That when vapour of sodium is present in space across which
light from another source is propagated, its atoms, according to a
well-known general principle of dynamics, are set to vibrate in
either or both of those fundamental modes, if some of the incident
light is of one or other of their periods, or some of one and some
of the other ; so that the energy of the waves of those particular
qualities of light is converted into thermal vibrations of the
medium and dispersed in all directions, while light of all other
qualities, even though very nearly agreeing with them, is trans-
mitted with comparatively no loss.

(5) That Fraunhofer's double dark line D of solar and stellar
spectra is due to the presence of vapour of sodium in atmospheres
surrounding the sun and those stars in whose spectra it had been
observed.

(6) That other vapours -than sodium are to be found in the
atmospheres of sun and stars by searching for substances producing

CHAP, ix.] LINES OF THE SOLAR SPECTRUM. 333

in the spectra of artificial flames bright lines coinciding with other
dark lines of the solar and stellar spectra than the Fraunhofer
line D.

Studying from this point of view the dark lines of the solar
spectrum, Bunsen and Kirchhoff were enabled to prove the coin-
cidence of a great number of them with the bright lines of certain
metals. For example, the seventy bright lines of iron, different in
colour, width, and intensity, coincide, in every point of view, and
precisely in the same way, with the seventy dark lines of the sun ;
which makes it impossible to doubt that, in the solar atmosphere,
iron exists in the state of vapour. In Fig. 240, a certain number
of these lines are seen, marked Fe. The same savants discovered
the presence of nine other simple bodies in the atmosphere of the
sun, — hydrogen, copper, zinc, chromium, nickel, magnesium, barium,
calcium, and sodium; and it is probable that to this list we may
add cobalt, strontium, and cadmium. This work has recently been

extended by the researches of Angstrom and Thalen. From the
absence of the characteristic lines of other metals, such as gold,
silver, platinum, &c. in the solar spectrum, it was believed, at first,
that these bodies are not found in the sun, at least in the outer
strata which form its atmosphere ; but this conclusion is too absolute,
as is shown by new researches due to M. Mitscherlich, which may
probably be explained by the observations of Frankland and Lockyer
before alluded to.

We sum up then what we have stated, as follows : —
Solids, liquids, and vapours and gases when dense, give us con
tinuous spectra without bright lines. Vapours and gases when not
dense give us continuous spectra with bright lines.

Changes in the lines composing the spectrum, and in the thickness
of the lines, are brought about by changes of pressure.

Gases and vapours absorb those rays which they themselves emit if a
brighter light source is behind them ; this absorption is continuous or
selective, as the radiatimi is continuous or selective.

This is one among many results brought about by employing
many prisms to give considerable dispersion, and therefore a very
long spectrum. There is another which reads almost like a fairy
tale ; so impossible does it at first sight appear, that we can thus
measure the velocities of the stars in their paths, or the rate at

334 PHYSICAL PHENOMENA. [BOOK in.

which solar storms travel by such means : but of this, more
presently.

One of the recent advances in the application of the spectroscope
to the examination of the celestial bodies arises from the following
considerations : —

The light from solid or liquid bodies is scattered broadcast, so
to speak, by the prism into a long band of light, called a con-
tinuous spectrum, because from one end of it to the other the light
is persistent.

The light from gaseous and vaporous bodies, on the contrary,
is most brilliant in a few channels ; it is husbanded, and, instead of
being scattered broadcast over a long band, is practically limited to
a few lines in the band — in some cases to a very few lines.

Hence, if we have two bodies, one solid or liquid and the other
gaseous or vaporous, which give out exactly equal amounts of
light, then the bright lines of the latter will be brighter than those
parts of the spectrum of the other to which they correspond in
colour or refrangibility.

Again, if the gaseous or vaporous substance gives out but few
lines, then, although the light which emanates from it may be much
less brilliant than that radiated by a solid or liquid, the light may
be so localized, and therefore intensified, in one case, and so spread
out, and therefore diluted, in the other, that the bright lines from
the feeble light source may in the spectroscope appear much brighter
than the corresponding parts of the spectrum of the more lustrous
solid body. Now here comes a very important point : supposing the
continuous spectrum of a solid or liquid to be mixed with the dis-
continuous spectrum of a gas, we can, by increasing the number of
prisms in a spectroscope, dilute the continuous spectrum of the solid
or liquid body very much indeed, and the dispersion will not
seemingly reduce the brilliancy of the lines given out by the gas :
as a consequence, the more dispersion we employ the brighter
relatively will the lines of the gaseous spectrum appear.

Let us apply this to the prominences seen round the sun in an
eclipse.

The reason why we do not see the prominences every day is that
they are put out by the tremendous brightness of our atmosphere
near the sun, a brightness due to the fact that the particles in the

CHAP, ix ] LINES OF THE SOLAR SPECTRUM. 335

atmosphere reflect to us the nearly continuous solar spectrum. There
is, as it were, a battle between the light proceeding from the promi-
nences and the light reflected by the atmosphere, and, except in
eclipses, the victory always remains with the atmosphere.

We see, however, in a moment, that by bringing a spectroscope
on the field we might turu the tide of battle altogether, since the
prominences are gaseous, as the reflected continuous spectrum is
dispersed almost into invisibility, the brilliancy of the prominence
lines scarcely suffering any diminution by the process. This reason-
ing was first successfully put to the test by a distinguished French
physicist, M. Janssen, in 1868.

Is it not wonderful, that the dispersion of light not only explains
with such accuracy the chemical composition of the bodies whence
it emanates, and preserves, after a passage of millions upon millions
of miles, the traces of absorption of various rays, — a certain indi-
cation of the presence of simple bodies suspended in an atmosphere
which astronomers only suspected, and the existence of which is
thus confirmed, — but enables us to measure velocities, and even to
study the meteorology of our sun ? as we shall see shortly. Spec-
trum analysis thus applied to sun, stars, planets, nebulae, comets,
furnishes valuable indications as to the intimate constitution of
these bodies, and solves problems which the most powerful optical
instruments would doubtless never have unravelled.1 It is thus
that the sciences mutually help each other: progress realized by
one of them is nearly sure to promote new discoveries in others.

1 For fuller particulars on this branch of the inquiry see " The Heavens," a
companion work to this.

336 PHYSICAL PHENOMENA. . [BOOK in.

CHAPTEE X.

SOLAR RADIATIONS. — CALORIFIC, LUMINOUS, AND CHEMICAL.

Divisions of the spectrum ; maximum luminous intensity of the spectrum —
Obscure or dark rays ; heat rays : chemical rays — Fluorescence, calorescence.

THE different parts of the solar spectrum are distinguished not
only by the unequal refrangibility of the rays which produce
them, by their colours, and by the greater or less vividness of their
brilliancy, but by their warming or calorific action, as well as by
their power of modifying, to different degrees, certain substances in
a chemical point of view.

When the luminous intensities of the seven principal colours
are compared together in the same spectrum, we at once perceive
that the brightest portion is found in the yellow. From this
point the brightness diminishes towards the red and the violet.
We see, moreover, that the colours can be naturally divided into
two classes : the first comprising the more luminous colours, red,
yellow, and green; the second, the darker colours, blue, indigo, and
violet ; there are continuations of the spectra in both directions
which are invisible to the eye. Thus we have the ultra-red and
the ultra-violet rays. In fact we must look upon the spectrum as
composed of heat-rays, light-rays, and chemical rays, the second
only of which are completely visible to us. A very simple experi-
ment enables us to judge of the difference which exists between
the illuminating powers of different colours : if we take the pages
of a book, and receive the spectrum on the printed portion of the
paper, we shall find that the characters can be easily read in the
orange, yellow, and green; whilst it is scarcely possible to read
those which receive the other colours.

According to Fraunhofer, who studied photometrically the

CHAP, x.] SOLAR RADIATIONS. 337

luminous intensities of the colours of the spectrum, the maximum
brightness is found between the lines D and E; but this point is
nearer D, and its distance from that line is about the tenth
part of the total interval D E. More precise methods have deter-
mined numerically the illuminating power of the spectrum at the
points where it is cut by the eight principal lines of Fraunhofer.
Taking the maximum brightness at a thousand, the following are
the luminous intensities : —

Colours. Luminous intensities. Lines.

Extreme red imperceptible A

Red 32 B

Red . . 94 0

Orange 640 D

Yellow 1000

Green 480 E

Blue 170 F

Tndigo 31 G

Extreme violet 6 H

This refers only to the relative intensities of the colours of the
solar spectrum, not to those of other spectra, nor to the similar colours
of various substances. These are pure colours, without mixture of
white or black: mixtures of black with primitive colours include,
as we have seen in explaining the classification of colours by
M. Chevreul, all the category of dark colours called browns, the
tints of which are no longer those of the corresponding ones in the
spectrum : the same holds with clear and bright colours obtained
by increasing proportions of white.

Some time ago the question arose whether the heat of the solar
rays was equally distributed throughout the whole length of the
spectrum, or if, on the contrary, the differently coloured rays, be-
sides their difference of luminous intensity, also possessed unequal
calorific powers. Some experiments made by the Abbe Eochon
led to the belief that the most luminous rays were also the most
calorific, so that the maximum heating was in the yellow; but
other physicists asserted that this maximum was in the red, or
rather beyond the extreme red. According to Seebeck (1828), all
these opinions are true, because heat, transmitted by the coloured rays,
being unequally absorbed according to the nature of the prism, the

D D

338 PHYSICAL PHENOMENA. [BOOK m.

position of the maximum calorific rays must depend on the sub-
stance of this latter ; and indeed, this physicist showed that the
most intense calorific rays are those of the yellow, orange, red, or
extreme red, according as the solar light is dispersed by the aid of
prisms formed with water, sulphuric acid, ordinary glass, or English
flint-glass. As rock-salt absorbs little or no heat, either dark or
luminous, the calorific powers of the differently coloured rays can be
best compared by using a prism of this substance. Working thus,
Melloni proved that the temperature of these rays increases in
passing from the violet to the red; and that the maximum calorific
effect is produced beyond the red, at a distance from the extreme
limit of the red equal to that which exists between this and the
yellow. Beyond this point the heat decreases; but it is still per-
ceptible when it has reached a distance from the red equal to the
whole extent of the luminous — that is, the visible — spectrum.

This remarkable result acquired a fresh degree of importance
when the solar rays were studied from another point of view.
We all know the influence of sunlight on material colours, when
these colours are given either to stuffs, paper, wood, or other organic
substances. Coloured curtains fade with daylight ; yellow cotton or
linen is bleached when exposed to the sun. We understand, in
the present day, how necessary light is to the complete develop-
ment of health, and even to the life of vegetables and animals.

Now, these multiple influences, to which we shall have occasion
to return, consist in a series of chemical actions in the decomposition
or combination of substances. Chlorine and hydrogen, which in
the dark have no action on each other, combine when exposed to
the light, forming hydrochloric acid. If the flask which contains
them is exposed to the diffused daylight, the combination is effected
slowly; in the solar rays, it takes place suddenly, and explosion
is the result. Light decomposes salts of gold, silver, and platinum.
Heliography, which was discovered by Niepce and Daguerre, and
all actual processes of photography, are based on the chemical
action of luminous rays, either from the sun, moon, or other suffi-
ciently intense luminous source. We shall describe these further on ;
we will now indicate the phenomena themselves. Mr. Eutherford,
who has photographed the spectrum with unequalled success, has deter-
mined that the maximum chemical effect lies near the line G.

CHAP, x.] SOLAR RADIATIONS. 339

The same question presents itself here as in regard to the
illuminating and heating effects. We require first to know if the
different regions of the solar spectrum are endowed with the same
faculty of chemical action, or if this efficacy varies in different parts
of the spectrum. Now Scheele, who in 1770 had ascertained the
action of light on chloride of silver, discovered also that the coloured
rays of the spectrum act unequally in producing this decomposition.
It was afterwards discovered, not only that the chemical rays
increase in intensity in passing from red to violet to such a degree
that the chloride in question blackens- in a few minutes, when it
receives the concentrated rays of the violet part of the spectrum,
whilst it requires several hours, if it receives rays between and
including the green and red rays, but that beyond the extreme
violet, in the dark portion of the spectrum, chemical action con-
tinues at a considerable distance beyond the luminous portions.

The intensity of chemical radiation, which varies for one substance
according to the position of the rays in the spectrum, does not
attain its maximum at the same point for different substances.
This maximum is not the same for salts of silver as for salts of
gold, nor for the latter as for salts of potassium.

The following phenomenon is worthy of remark : the spectrum
which may be called chemical, to distinguish it from the luminous
and heat spectrum, possesses rays like the luminous spectrum. In the
dark portions of a spectrum photographed by means of chloride of
silver, white lines may be observed which indicate an interruption
of chemical action, and their position coincides precisely with Fraun-
hofer's lines. But, beyond the violet, other lines exist, which naturally
have no corresponding ones in the luminous spectrum.1

Professor Stokes, by enabling us to see these invisible rays, has
given us the reason why they are ordinarily invisible. If we receive
these rays on a screen washed with a solution of sulphate of quinine,
they are at once visible as blue light ; we have the phenomenon of
fluorescence, which can also be rendered visible by other means.

The explanation of the phenomenon of fluorescence is that the
ultra-violet rays, which move too rapidly for our eyes, have their

1 Nevertheless, the most refrangible rays, like the violet, are not completely
invisible. According to J. Herschel, the ultra-violet rays, acting on the retina,
give a shade called by him lavender-grey.

D D 2

340 PHYSICAL PHENOMENA. [BOOK in.

velocity retarded — toned down when they fall on and are reflected
from sulphate of quinine — and are thus brought within the range
of visibility and known colour. The heat rays have been similarly
rendered visible by Professor Tyndall in the phenomenon of calor-
escence, in which the obscure heat rays have their velocity increased.

Thus, the solar spectrum is more complete than was at first
believed, from studying only the impressions produced on the eye. It
appears to be formed of three superposed spectra ; one giving light
and colours ; another, the action of which is sensible to the ther-
mometer, revealing to us the warning or calorific property of the
solar rays; and the third teaching us how much their chemical
activity varies. But, do three kinds of rays exist, as was at first
supposed ? Delicate experiments, among which we only quote that
which implies the identity of the rays of the luminous spectrum
and those of the chemical spectrum, prove that there is identity
between the different radiations. The same rays produce, in one
place, varied colours ; in another, varied luminous intensities :
here, unequally distributed intensities of heat; there, chemical
combinations and decompositions. Only, a ray, which is endowed
with considerable calorific and chemical power, does not excite in
us the luminous sensation, or rather, only exercises on our retina
an inappreciable influence. Thus, as there are sounds in Nature to
which our ears are not attuned, so are there colours in the spectrum
which will for ever remain invisible to us.

CIJAP. XL] PHOSPHORESCENCE. 341

CHAPTER XL

PHOSPHORESCENCE.

Phenomena of spontaneous phosphorescence — Animal and vegetable phosphores-
cence— Glow-worms and fulgurse ; infusoria and medusae — Different conditions
which determine the phosphorescence of bodies — Phosphorescence by insola-
tion— Becquerel's phosphoroscope.

WE have already alluded to fluorescence ; there is another curious
phenomenon which differs from fluorescence in this, that it
remains for long after the exciting source of light is withdrawn.
The history of the discovery of phosphorescence is as follows : —

In 1677, an alchemist of Hamburg, named Brandt, discovered
by a process which he at first kept secret,1 a new body endowed,
among other singular properties, with the property of emitting a
continuous luminous smoke when it was exposed to the air. Hence
the name phosphorus (from <£&>?, light ; <£e/oo>, to bear) applied
to this substance, which is one of the sixty-four simple bodies now
recognised. If we trace characters on a wall with a stick of
phosphorus, they will appear as luminous lines in the dark, and
will not cease to shine until after the complete disappearance, either
by slow combustion or evaporation, of the phosphorescent matter.

Long before the discovery of this body, the name of phosphori
was given to all substances which, like it, emitted light without
being accompanied by sensible heat ; such as wood, decomposed
by the action of moisture ; dead salt-water fish not yet putrified,
the shining of which is communicated to the water itself, when it
is agitated for some time; and lastly, a great number of mineral

1 A few years after Brandt, Kunckel discovered the means of obtaining phos-
phorus. A century later, in 1769, Scheele proved that it exists in abundance in
the bones of men and animals.

342 PHYSICAL PHENOMENA. [BOOK in.

substances, when they are submitted to blows or to mechanical
friction, or when they have been exposed to the solar rays.

It is to this emission of spontaneous or artificial light that
physicists have given the name of phosphorescence. Phosphorescence
is not peculiar to inorganic or lifeless matter. When, on a warm
evening in June or July, we walk in the country, it is not
uncommon to s.ee in the grass and under the bushes a multitude
of small lights, which shine like terrestrial stars : these are the
lampyres, or glow-worms, a species of coleoptera, the larvae of which,
like the perfect insect, but in a less degree, possess the property
of emitting a greenish blue light. The fulgura or lantern fly, and
the cucuyos of Mexico and Brazil, shine during the night with a
light sufficiently bright to enable one to read. Certain flowers,
like the flowers of the marigold, nasturtium, and Indian rose, have
been considered as phosphorescent, but it how appears to be proved
that this is a mistake ; it is certain that fifteen phanerogamic plants,
and eight or nine cryptogamic ones, emit light ; but only in the
evening after they have been receiving the sun's light ; so that
exposure to the sun appears to be to them a condition essential to
phosphorescence. The phosphorescence of the sea is produced by
myriads of animalculse, which, like the lampyres and fulgurae,
emit a light sufficiently bright to give to the waves the appearance
of fire. It is now infusoria, now medusae, starfishes, &c., which
diffuse, some a blue, others red or green lights, or even give the
sea a whitish tint, to which sailors give the name of sea of snow
or sea of milk.

Calcined oyster-shells become luminous when they are exposed
to the light of the sun ; this property is due to the sulphide of
calcium; it is also possessed by the sulphides of barium and
strontium.1

Phosphorescence can be induced in a great many substances
by mechanical or chemical action; this may be noticed on break-
ing sugar, the light being produced at the moment of rupture.

1 Canton, an English physicist, discovered in 1764 the phosphorescence of
calcined oyster-shells ; hence the sulphide of calcium is called Canton's phosphorus.
V. Calciarolo, a workman of Bologna, discovered the phosphorescence of calcined
sulphate of baryta ; hence the name Bologna phosphorus which is given to sulphate
of barium.

CHAP, xi.] PHOSPHORESCENCE. 343

Similar effects are produced by rubbing two pieces of quartz against
each other, also chalk, or chloride of calcium, or on separating
plates of mica by cleavage. Elevation of temperature also pro-
duces phosphorescence. Fluorspar, diamonds and other precious
stones, chalk, sulphate of potassium and quinine, emit light when
they are placed in contact with warm substances. We shall see
further on, that electricity is able to produce the same effects in
bodies which are bad conductors.

Thus we have a series of phenomena in which the production
of light is neither the result of rapid combustion at a high tem-
perature, nor that of a vivid illumination which disappears as
soon as the source ceases to be in the presence of the illumined
object. All the bodies which we have mentioned, and which
peculiar circumstances render phosphorescent, acquire, for a limited,
but often considerable time, the property of being luminous by
themselves, of emitting light perceptible in the dark, and strong
enough to illuminate objects lying near them.

Phosphorescence appears to be due to multiple causes: in
organized and living beings, the mode of producing light is nearly
unknown. We only know that the will of the animal plays a
certain part, that a moderate temperature is necessary to the
emission of the light, as also is the presence of oxygen gas. A
sharp cold or intense heat both cause it to disappear. In phos-
phorus, decayed wood, dead fish, &c., the production of light is
doubtless due to chemical action, — that is, to slow combustion ;
for, in vacuo, all phosphorescence ceases. It follows therefore,
from the facts above stated, that exposure to the sun, elevation
of temperature, electricity, and mechanical action, in which elec-
tricity and heat doubtless take part, are, in many cases, favourable
conditions to the development of phosphorescence. This singular
mode of production of light has recently been the subject of very
interesting studies by MM. Biot, Matteucci, and principally by M.
Edmond Becquerel. We will rapidly glance at some of these.

It has long been known that phosphorescence is a property
which can be momentarily acquired by a number of bodies,
especially in a solid or gaseous state : paper, amber, silk, and a
multitude of other substances of organic origin ; oxides and salts
of alkaline and earthy metals, and of uranium ; and a great many

344 PHYSICAL PHENOMENA. [BOOK in.

gases. But no other metals, nor their compounds, nor any other
kind of liquid, has up to the present time manifested the slightest
trace of this phenomenon.

The tints of phosphorescent light vary according to the nature
of the body which emits it: thus precious stones emit a yellow or
blue light; sulphides of strontium, barium, and calcuim give all
the shades of the spectrum, from red to violet. But a singular
fact proved by M. Ed. Becquerel is, that the tint and brightness
of the light do not depend alone on the temperature, but also 011
the mode of producing the sulphides, and, what is still more singular,
on the molecular state of the salts whence they have been produced.
Thus, having taken different carbonates of lime, spar, chalk, &c.,
and having treated them with sulphur, he obtained six sulphides
of ^calcium which, exposed to the sun, became phosphorescent, and
in darkness presented the following tints: —

Tint of the Light.

Iceland spar Orange yellow

Chalk . . . . ; V . , . Yellow.

Lime . . . . ;v . . . Green.

Fibrous arragonite .... Green.

Marble . . ^ . .' : Rose violet.

Arragonite of Vertaison . . Eose violet.

" If I may be allowed the comparison," . says M. Edmond
Becquerel, in regard to these facts, " I could say that these last
bodies, on account of their luminous effects, are analogous to the
sonorous cords which produce different sounds according to their
tension."

Elevation of temperature accelerates phosphorescence, but it also
exhausts it quickly : for the light obtained does not last long. It
has also the effect of modifying the tints ; thus sulphide of strontium,
blue at the ordinary temperature, passes to a blue violet, clear blue,
green, yellow, and lastly to orange, when its temperature is raised
from 20 degrees below zero to 150 degrees above.

It will be of much interest to study the manner in which the
different rays of the spectrum act on bodies in determining their
phosphorescence, from the chemical rays situated in the dark part
of the spectrum beyond the violet, to the heat-rays beyond
the red. In order to observe this, the spectrum is projected on
a band covered with various phosphorescent substances, and the

Sulphides of

Calcium obtained

from

CHAP. XT.]

PHOSPHORESCENCE.

345

luminous effects produced are examined in the dark at different
distances, that is to say, in the regions covered by the prismatic
rays. Thus, it is possible to ascertain which of the rays produce
the most intense luminous effects. It is found that the maxi-
mum of action depends on the bodies influenced ; but in every
case, the chemical rays nearest the violet, and consequently the
most refrangible, produce phosphorescence : the heat-rays do not
excite it ; but they are endowed with the property of continuing
the action of the chemical rays. These results explain the feeble

FIG. 242. — M. Ed. Becquerel's phospnoroscope.

action of the flames of candles, or gas, in producing the phosphor-
escence of bodies, and, on the other hand, the efficiency of the
electric light : this latter abounds in chemical and ultra-violet rays,
whilst the former, although rich in heat-rays, are very poor in
chemical rays. The bright light of magnesium rivals, as M. Le
Eorey proves, the electric light. It is sufficient to burn a wire

346 PHYSICAL PHENOMENA. [BOOK in.

of this metal in presence of a tube inclosing, for example, some
sulphide of calcium, to obtain prolonged phosphorescence, as may
be shown by carrying the tube into darkness.

M. Edmond Becquerel invented, for the study of these phenomena,
an instrument which he calls the phosphoroscope. The following is
a short description of it : — Two blackened discs are each pierced
with four openings in the form of sectors, and can be caused to
revolve on a common axis : but as the openings of one do not cor-
respond with the openings of the other
(as may be seen in Fig. 243), it follows
that a ray of light cannot pass through
the system of the two discs, whatever
may be the rate of rotation. They are
both inclosed in a blackened box, which
remains fixed, and in the sides of which
are two openings. The solar light passes
through one of them, falls on the body,
the phosphorescence of which is to be

Fio. 243 —Disc of the phosphoroscope. T i -i i • i • r> -i -i

studied, and which is nxed between the

two discs, in the axis of -the outer openings of the box ; but, as
we have said, it cannot pass through the other side.

The phosphorescent light induced in the body passes, on the
contrary, through the opposite opening every time the rotatory
movement brings one of the movable windows in front of the
outer opening. The action of light on the body is thus produced
four times during each revolution. If the velocity is sufficient, the
developed phosphorescence is continuous, and the sensation produced
in the eye of the observer is equally so.

The phosphoroscope, thus constructed, gives to the body observed
a constant quantity of light, whatever the rotatory movement may
be ; the quantity of phosphorescent light which reaches the
eye is also constant ; but the duration of the constant action
of the light on the body varies with the velocity, as it is equal
to the time that an opening takes to pass before it : this duration
is easily measured when one knows the dimensions of the opening
and the number of turns that the system of the two move-
able discs makes in one second. To sum up : the more rapid the
rotation, the shorter the duration of the light, but the interruptions

CHAP. XL] PHOSPHORESCENCE. 347

in this action are shorter, so that there ought to be a certain
velocity for which the maximum brilliancy is obtained.

By the aid of the phosphoroscope, M. Becquerel, besides the
result we have already described, has been able to prove the existence
in some bodies of luminous emissions, the duration of which does
not exceed the ten- thousandth part of a second. Others, like the
green sulphide of strontium and calcium, remain phosphorescent
for thirty-six hours. Diamonds shine for many hours. He has
been able to study the law according to which, the phosphorescent
bodies lose their light by successive emissions.

The light emitted by various vegetable and animal phosphor-
escents has been submitted to spectrum analysis; and it is found
that the spectra of these lights are continuous, as neither dark
nor bright lines can be distinguished.

348 PHYSICAL PHENOMENA. [BOOK in.

CHAPTEE XII.

WHAT IS LIGHT?

TTITHERTO we have described luminous phenomena as studied by
_L_L observation, without indicating any hypothesis regarding the
particular nature of the agent which induces the perception of these
phenomena by our organs. All that we know is, that the various
substances in Nature can be ranked in two classes : in the first
are placed light-sources, or bodies capable of producing light
directly and of themselves ; in the second, bodies which transmit in
divers ways the light MLing on them, but which, in their actual state,
cannot directly emit it.

Among light-sources, there are some, like the sun and most of
the stars, which appear to be constant, — at least their emissive power
has not decreased for thousands of years : probably we ought to
count by millions of centuries, if we wish to measure the probable
duration of this power. But they doubtless do not differ essentially
from temporary luminous sources which we have at our disposal on
the surface of the globe. These latter owe their state either to a very
high temperature, to chemical combinations conducive to the disen-
gagement of light, such as a furnace, or to a state of electric tension
producing the same result — take the electric light. All that we know
of the physical constitution of the sun, and say, a white-hot cannon-
ball or any mass of metal, tends to prove that they are globes in a
state of incandescence. We have already seen that, among the
substances of the second class, there are many which can momen-
tarily acquire, under the influence of temperature, e^osure to the

CHAP, xir.] WHAT IS LIGHT? 349

sun, or certain chemical or mechanical actions, the property of
emitting light, which is called phosphorescence ; and that without
being in a state of incandescence or vivid combustion.

We know also that light is not transmitted instantaneously, but
that it requires a definite time to pass from one point to another — in
a word, that it has a particukr mode of movement. We have now,
therefore, to inquire in what this movement consists ; that is, whether
light is a substance incessantly emitted by luminous bodies, or an
impulse produced in a special medium, and propagated through space.
These are questions of such great interest, that they necessarily force
themselves upon the mind ; their examination will also have the
advantage of furnishing us with an explanation of various phenomena
to be hereafter described. The time has therefore arrived for us to
indicate the nature of a theory now generally received by physicists,
and by the help of which all optical phenomena are found to be
consequences of a single principle. At the same time, we may give
certain details concerning another hypothesis, which for a length
of time had the privilege to share with the first a common applic-
ability to optical phenomena. We will first consider the older theory,
known as the emission theory.

According to Newton, who first reduced this theory to a system,
light is formed of material molecules of extreme tenuity, which are
perpetually emitted by luminous bodies, and which the latter project
through space with a uniform velocity; the impact of these pro-
jectiles on the retina agitates the optic nerves, and produces in us
the sensation of light. These particles are endowed with attractive
and repulsive forces, which are manifested in the neighbourhood of
the molecules of bodies, and produce the attractive forces of interior
refraction and reflection, and the repulsive forces of exterior reflec-
tion. There are as many kinds of particles as colours, and each
kind possesses a particular refrangibility.

Successive particles which follow the same right line form a
luminous ray ; but they may be separated by great intervals. The
luminous impression has been proved to remain on the retina about
one-tenth of a second; it is therefore sufficient that ten luminous
particles should arrive at the eye in a second, in order that the
impression caused by one of them should not be effaced before the
arrival of the next; or, which is the same, in order that there shall

350 PHYSICAL PHENOMENA. [BOOK in.

be a continuous sensation. Supposing them situated at equal dis-
tances, they should follow each other at a distance of 18,600 miles
from each other. Supposing they follow each other at the rate of
a hundred a second, there would still be an interval between them
of 1,860 miles.

We understand, therefore, how, according to this hypothesis, the
luminous rays emanating from different sources can intersect each
other in various directions without obstruction. But we must suppose
that the mass of each of them is of such small weight, that our imagi-
nation can scarcely realize the idea. Sir J. Herschel assisted it by
the following comparison. He says : " If a molecule of light weighed
one grain (0*065 gramme), its effect would be equal to that of a
cannon-ball of 150 Ibs. (56 kilogrammes), animated by a velocity
of 305 metres (330 yards) per second. "What, then, must this tenuity
be, if a thousand million of molecules, attracted by lenses and mirrors,
have never been able to communicate the least movement to the most
delicate instruments invented expressly for these experiments ! "
(Treatise on Light, vol. i.) Sir John Herschel lived indeed before the
discovery of the Radiometer.

"We have just stated that, to explain the phenomena of reflection
and refraction of light, Newton imagined that each molecule is either
repelled or attracted by the molecules of bodies. The intensity of
these forces, which are exerted in infinitely small spheres, is pro-
digious ; it is proved that they exceed the intensity of gravity at
the surface of the earth to such a degree, that it is necessary, in
order to express their value in numbers, to multiply this latter
intensity by the figure 2, followed by forty-four zeros.

In the theory which is now adopted, — the undulatory theory, —
we find numbers which submit somewhat to precedent ; it is not
difficult, therefore, to conceive that it has been preferred to the
theory of emission.

We owe the first exact exposition of the undulatory theory to
Huyghens, who numbered among his partisans, in the last centuries,
Hooke and Euler ; and among those who have developed and per-
fected it in the present century, Young and Fresnel. We will
endeavour to explain the undulatory theory in its essential elements.

The hypothesis of emission requires that the interplanetary
celestial spaces be void of matter, in order to give free passage to

CHAP, xii.] WHAT IS LIGHT? 351

the motion of the luminous molecules, or rather these spaces must
be free from all matter, save the molecules themselves. On the
other hand, according to the undulatory hypothesis, these same
spaces are filled with an extremely thin and eminently elastic fluid,
which is called the ether. This medium penetrates all bodies, and
is diffused throughout all the inter-molecular spaces.

Luminous bodies are those whose molecules, in a state of
continual vibration, communicate impulses to the ether, which, in
its turn, propagates the same vibratory movement from place to
place and in all directions, with a uniform velocity of 186,000
miles per second. The velocity of propagation of the lumi-
nous waves is the same for all the rays of light, whatever their
intensity or colour. It is uniform and constant in a homo-
geneous medium ; but it varies in passing from one medium
to another ; and, as it is admitted that it is dependent on the
connection which exists between the elasticity of the ether and its
density, it must be inferred that this connection itself changes in
different media; that is to say, the distribution of the molecules
of ether is not the same in interplanetary media as in heavy
bodies ; and in these it varies with the nature of the substances
and their density.

Let us try to understand the nature of the vibrations of the ether.

Each molecule of a luminous source executes a series of very
rapid vibrations ; that is to say, of backward and forward move-
ments across a position of equilibrium. These vibrations are
communicated to the ether, the different molecules of which assume
the vibratory movements similar to those of the light-source, and
communicate them spherically from place to place. During the time
which a molecule of ether requires to make a complete oscillation
round its position of equilibrium, its movement is communicated,
in the direction of the propagation of light, to a stream of molecules,
the most distant of which is at a fixed distance from the first : it
is this distance which is called the wave-length, and the luminous
wave is nothing more than the series of movements effected during
a complete oscillation of a molecule of ether. As the same dis-
turbance which has its origin at one point of the source of light
is thus propagated in the ether which fills space, with uniform
velocity, it follows that all points of the surface of a sphere,

352 PHYSICAL PHENOMENA. [BOOK m.

having for its centre the luminous point, are at the same instant in
the same phase of vibratory movement. All the points of any of
these spherical surfaces are called the surface of the wave. In
certain media, the surface of the wave can be ellipsoidal. Lumi-
nous waves have, therefore, great analogy with sonorous waves;
like them, they are isochronous, and they move with uniform velo-
city. They consist in alternating movements of an elastic medium
across a position of equilibrium ; but, whilst the vehicle of sound is
a tangible medium, as the air, or any other gaseous or liquid or
solid body, the vehicle of light is a substance, if not imponderable,
at least intangible.

The sonorous wave is propagated through the air, travelling in
a right line 330-6 metres per second ; the luminous wave, in the
same time, travels 186,000 miles, and, whilst the length of an un-
dulation varies, for perceptible sounds, between one-fifth of an inch
and eleven yards, the maximum length of an undulation of ether
does not attain the twenty-five thousandth part of an inch. But
between these two modes of vibratory movement there exists, as
Fresnel has shown, an important difference; for, whilst sonorous
vibrations are made in the same direction as their propagation,
luminous vibrations take place in a direction perpendicular to that of
the movement of propagation, that is, parallel to the surface of the
waves. It is difficult to imagine the vibrations being effected per-
pendicularly to the direction of their propagation. A comparison will
explain this kind of movement. If we take hold of the end of a
very long cord placed in a straight line along the ground, and give it
a shake in a vertical direction, there follows a series of undulations
which are propagated to the other extremity, all of which are effected
in a direction perpendicular to that of the cord, just as we see
undulations which succeed each other on the surface of the water
caused by the throw of a stone, or any other heavy body, on the
liquid. There is, between these two phenomena and the movement of
the ether, one resemblance more ; that is, that the propagation of the
waves takes place without there being any transport of the molecules
which undergo the vibration.

We shall presently understand how the wave-lengths of luminous
vibrations can be measured, and how it was discovered that these
lengths vary in passing from one colour to another. They are, as

SPECTRA OF THE METALS OF THE ALKALIES & ALKALINE EARTHS.

From the Drawings of BUNSEN & KiRCHHOFF.

10 20 30 40 SO 60 70 80 90 100 110 120 130 1-13 1C 3 1CD 170

Ka Lia

Sr3

Rb K.0

CHAP, xii.] WHAT IS LIGHT ? 353

the following table shows, excessively small, their mean value scarcely
ever exceeding the half of a thousandth of a millimetre. When
these wave-lengths are once known, an easy calculation gives the
number of vibrations which the ether performs in a second, when it
gives rise to the different colours of the spectrum. As light travels
over an interval of 298,000 kilometres (186,000 miles) in one second,
it is sufficient to divide this last number by each wave-length, in order
to find how many of these vibrations take place in a second.

Here are the results for the seven principal colours of the sola.r
spectrum : —

Ked, mean 620 ..... 514,000,000,000,000

Orange, „ 583 .' . . ft'V 557,000,000,000,000

Yellow, „ 551 "". •'. .-'/ ; .' 548,000,000,000,000

Green, „ 512 .... . 621,000,000,000,000

Blue, „ 475 ....>. 670,000,000,000,000

Indigo, t1 449 ..... 709,000,000,000,000

Violet, „ 423 ... ."'•'; ' 752,000,000,000,000 l

This determination of wave-lengths, combined with wide dis-
persion, enables us, by reason of the high velocity of some of the
motions of the heavenly bodies, — a velocity comparable with that
of light itself, — and the existence of bright and dark lines in their
spectra, to determine the rapidity of the various movements of many
of the stars.

Let us endeavour to give an idea how this result is arrived at,
begging indulgence for a gross illustration of one of the most
supremely delicate of nature's operations.

Imagine a barrack, out of which is constantly issuing with
measured tread and military precision an infinite number of soldiers
in single or Indian file; and suppose yourself in a street seeing
these soldiers pass. You stand still, and take out your watch, and
find that so many pass you in a second or minute, and that the
number of soldiers, as well as the interval between them, is always
the same.

You now move slowly towards the barrack, still noting what

1 These numbers are deduced from the new determination of the velocity of
light ; they exceed by about ^ those given in treatises on physics before the result
of M. Foucau It's experiments was known.

E E

354 PHYSICAL PHENOMENA. [BOOK in.

happens. You find that more soldiers pass you than before in
the same time, and, reckoned in time, the interval between each
soldier is less.

You now move still slowly from the barrack, i.e. with the soldiers.
You find that fewer soldiers now pass you, and that the interval
between each is longer.

Now suppose yourself at rest, and suppose the barrack to have a
motion, now towards you, now from you.

In the first case the men will be paid out, so to speak, more
rapidly. The motion of the barrack-gate towards you will plant each
soldier nearer the preceding one than he would have been if the
barrack had remained at rest. The soldiers will really be nearer
together.

In the second case it is obvious that the interval will be greater,

and the soldiers will really be further apart.

So that, generally, representing the interval, between each soldier
by an elastic cord, if the barrack and the eye approach each other
by the motion of either, the cord will contract; in the case of
recession, the cord will stretch.

Now let the barrack represent the hydrogen in Sirius or the
sun, perpetually paying out waves of light, and let the elastic cord
represent one of these waves; its length will be changed if the
hydrogen and the eye approach each other by the motion of either.

Particular wave-lengths with the normal velocity of light are
represented to us by different colours.

The long waves are red.

The short waves are violet.

Now let us take the case of the hydrogen in the sun and fix
our attention on the green wave, the refrangibility of which is
indicated by the F line of hydrogen. If any change of wave-length
is observed in this line, and not in the adjacent ones, it is clear that
it is not to the motion of the earth or sun, but to that of the
hydrogen itself and alone, that the change must be ascribed.

If the hydrogen is approaching us, the ivaves will be crushed
together; they will therefore be shortened, and the light will incline
towards the violet, that is, towards the light with the shortest waves ;
and if the waves are shortened only by the 1Qu^ouoth of a millimetre,
we can detect the motion.

CHAP. XTI.] WHAT IS LIGHT ? 355

If the hydrogen is receding from us, the waves will be drawn
out; they will therefore be longer, and the green ray will incline
towards the red.

In Sirius there is hydrogen, and by this means Mr. Huggins has
determined the velocity of that star's movement in the heavens.

Now, in the case of the sun, bear in mind that there are two
different circumstances under which the hydrogen may approach or
recede from the eye.

Take a globe, which we will consider to represent the sun. Fix
your attention on the centre of the visible hemisphere of this globe :
it is evident that an uprush or a downrush is necessary to cause any
alteration of wave-length. A cyclone or lateral movement of any
kind is powerless ; there will be no motion to or from the eye, but
only at right angles to the line of sight.

Next fix your attention on the edge of the globe — the limb, in
astronomical language : here it is evident that an upward or down-
ward movement from the centre of the globe outwards is as powerless
to alter the wave-length as a lateral movement was in the other case,
but that, should any lateral or cyclonic movement occur here of
sufficient velocity, it might be detected.

So. that we have the centre of the disc for studying upward and
downward movements from the centre of the globe outwards — upward
or downward as they would seem to a spectator standing on the sun,
and the limb for studying lateral or cyclonic movements, if they exist.

Now the hydrogen lines in the solar spectrum are observed to
change their places, while the lines near them remain at rest, so that
they may be looked upon as so many milestones telling us with what
rapidity the uprush and downrush takes place ; for the twistings in
the hydrogen lines are nothing more or less than alterations of wave-
length, and thanks to Angstrom's map, we can map out distances
along the spectrum from F in jowooo^h8 °^ a millimetre from the
centre of that line; and we know that an alteration of that line
io;ooo(oootns °f a millimetre towards the violet means a velocity of
38 miles a second towards the eye, i.e. an uprush ; and that a similar
alternation towards the red means a similar velocity from the eye,
i.e. a downrush.

To sum up : these are the two theories proposed for the explana-
tion of luminous phenomena. Both explain with equal facility the

E E 2

356 PHYSICAL PHENOMENA.

reflection and refraction of light ; but, whilst the system of emission
requires that the velocity of propagation should be greater in refractive
media, the undulatory theory, on the other hand, supposes that this
velocity is less, according as the medium is endowed with more con-
siderable refractive power. To decide between them, it is therefore
only necessary to determine the velocity of light in different media, to
settle, for instance, the following question : — Is light propagated
through air more or less rapidly than through water ?

Now, this important problem has received a definite solution
during the last few years. M. Foucault and M. Fizeau, each in his
turn, by a very ingenious process, the principle of which was first
employed by Wheatstone for calculating the velocity of electricity,1
has succeeded in proving that light is propagated with less
rapidity through water than through air, as the theory of undu-
lation requires.

Other phenomena, which we will now describe, are equally
favourable to this theory ; whilst, on the emission theory, no satis-
factory explanation of them can be found. It is no longer doubtful
that the preference ought finally to be given to the theory wliich
makes light not a particular substance projected through space by
luminous bodies, but a vibratory movement propagated through a
medium which fills space ; not only that space which is usually called
the interplanetary space, but that which is occupied by the interstices
of the molecules of ponderable bodies.

1 F. Arago conceived the idea of using Wheatstone's revolving mirror to com-
pare the velocities of light through different media.

CHAP, xni.] INTERFERENCE OF LUMINOUS WAVES. 357

GHAPTEE XIII.

INTERFERENCE OF LUMINOUS WAVES. — PHENOMENA OF DIFFRACTION.

GRATINGS.

Dark and bright fringes due to very small apertures — Grimaldi's experiment —
Interference of luminous waves ; experimental demonstration of the principle
of interference — Phenomena of diffraction produced by slits, apertures of dif-
ferent form and gratings — Coloured and monochromatic fringes.

IN 1665 Pere Grimaldi published at Bologna a curious work entitled
" Physico-Mathesis de Lumine," in which he described for the
first time appearances to which he gave the name, which they still
bear, of diffraction phenomena, which physicists have since studied
and multiplied until they form an important branch of optics.

Having introduced a beam of light into a dark room through a
very small aperture, Grimaldi noticed that the shadows of narrow
opaque bodies exposed to this light were spread out much more than
they should have been. Besides, these shadows were edged with
coloured fringes, parallel to themselves and to the edges of the
opaque bodies. The phenomenon disappears if, instead of a narrow
aperture, the pencil of light passes through a wide hole.

If we substitute for the opaque body a very small circular hole,
made for instance in a metallic plate, and receive the light which
has passed through it on a screen, concentric rings with, coloured
fringes are obtained, some situated within the geometric image of
the aperture, others beyond ; that is to say, within the limits of the
shadow of the plate. Thus, two apertures placed near together give
two series of rings, which partly overlap each other; and, moreover,
three series of dark rectilinear fringes or bands are perceived, which
disappear directly one of the holes is moved (Fig. 244). This last
experiment caused great astonishment in the philosophic world, as it

358

PHYSICAL PHENOMENA.

[BOOK m.

upset all the ideas then conceived as to the nature of this luminous
agent. And, indeed, it seemed to show, that light added to light
produces, in certain cases, DARKNESS !

Newton studied the phenomena of
diffraction discovered by Grimaldi; and
he added fresh observations, and endea-
voured to explain the cause of diffraction
by a deviation when the edges of opaque
bodies are subjected to the rays of light.
Fraunhofer, Young, and Fresnel suc-
ceeded in discovering the laws, and the
last-named connected them in the most
happy manner with the undulatory theory.
Before continuing the description of the
phenomena, let us endeavour to form some
idea of what Young called the principle
of interference — the theory of which

he has clearly explained on the undulatory hypothesis, and
which Fresnel afterwards demonstrated by the famous experiment
of the two mirrors.

Let us suppose that two rays of light follow the same direction,
A B ; that they have the same intensity, and that the wave-lengths
of each of them are equal, in which case the vibratory movements of
the ether will have the same amplitude for the same phases. If the

FIG. 244. — Grimaldi's experiment.
Dark and bright fringes produced
by a system of two small circu-
lar holes. /

FIG. 245. — Interference of luminous waves.

waves of the first ray coincide with those of the second, it is clear
that their intensities will become united ; the quantity of light will
be increased by their union. But if one of them is behindhand
precisely half the length of a wave, the molecules of ether situated
along the line A B will be drawn from one side by forces the intensity

CHAP, xiii.] INTERFERENCE OF LUMINOUS WAVES. 359

and direction of which will be represented by the curve a a a ....
and from the other side by equal and contrary forces represented by
the curve a a a'. ... Every molecule, such as m, will then remain
at rest under the action of these opposed forces : the vibratory move-
ment will cease, and darkness will succeed to light. It is then said
that the luminous waves or rays interfere.

The same result is produced if the retardation is f , J . . . and
generally, odd numbers of half undulations. If it be an even num-
ber of half undulations, the result is the same as if there had been
coincidence. Thus, between these two extreme cases, the luminous
intensity is sometimes increased and sometimes diminished, but in
neither case is there an absolute destruction of light.

Theoretically, this reasoning, which is a necessary consequence
of the undulatory theory, perfectly accounts for Grimaldi's experi-
ment, and all those in which dark and bright fringes or bands appear.
It nevertheless had to be proved by observation, and this Fresnel
accomplished, mainly by the experiment of the two mirrors we
have already mentioned. This experiment is too important for us
to neglect here. The nature and limits of this work do not permit
us to touch upon theoretical explanations of many phenomena,
but the principle in this instance must at least be described with
sufficient clearness to enable the reader to accept the inferences
with confidence.

Two plane mirrors, o N, o M (Fig. 246), of metal or black glass, are
placed vertically in a dark room, so as to form an angle much more
obtuse than in the figure. In front of these mirrors a beam of sunlight
is brought to a focus at s by a spherical or cylindrical lens, so that it
can give either a point or a luminous line. Two images are thus
formed, one in each mirror ; that in s for the mirror o N, the other in
s for the mirror 0 M.

We have thus two sources of light which present this peculiarity,
that, as they emanate from a common source, they are in the same
state of vibration. If we now place a vertical screen in front of
the mirrors, in such a way as to receive the luminous beams from the
two images, a bright band will be perceived on the screen in the pro-
longation of the line o A, and, on each side of this band, a series of
alternate dark and bright fringes. If one of the mirrors is taken away,
the fringes instantly disappear, and the screen is evenly illuminated.

300 PHYSICAL PHENOMENA. [BOOK in.

It is thus seen that the phenomenon is the same as in Grimaldi's
experiment of the two openings, and it remains for us to explain how
light added to light can produce darkness ; or, as we have seen, that
whenever dark fringes occur, it is due to the interference of luminous
waves emanating from two sources, and that, on the other hand,
we have the same phase of undulation whenever bright fringes or

FIG. 246.— Fresnel's experiment of two mirrors ; experimenal demonstration of
the principles of interference.

bands are seen. Figure 246, in which we observe concentric
waves emanating from s and s' , explains this. These two sys-
tems of waves cross and cut each other at different points. Now,
such of these points which, like a, are situated on the perpendicular
A o to s s , are in the same phase of undulation in both systems,
since the rays s a, s a, being of the same length, the same paths
sia and si' a are followed by the two luminous waves emitted

CHAP. xui.J INTERFERENCE OF LUMINOUS WAVES. 361

from the one source s, and reflected by both mirrors. The same takes
place with regard to the points a a a' . . . situated in the vertical
plane passing through A 0.

The luminous intensities are therefore united in this plane ; hence
the central bright fringes. In positions such as n, n' , the difference
of path of the waves which cross each other is from £,§...
wave-lengths ; in other words, an odd number of half undulations :
hence interference ensues, and consequently a dark band. It is so
also for the points mm'.... wherever a dotted arc cuts a plain arc
in the figure. Further on, the points & b' . . . c c . . . belong to rays
each of which is delayed an even number of half wave-lengths behind
the other ; hence bright fringes . . . and so on.

In order to try this admirable experiment, Fresnel used in suc-
cession lights of all the simple colours ; he found fringes of each
of these tints, but they became narrower as he got farther from
the red in the series of prismatic colours. Violet gave the nai>
rowest bands. By measuring with great precision the distances
of the bands, this illustrious physicist succeeded in deducing
the wave-lengths of light of different colours, and afterwards the
number of vibrations executed by the ether in the short interval of a
second — the wonderful numbers we have already seen. Fringes pro-
ceeding from white light ought therefore to be formed of fringes
coloured by each of the spectrum tints superposed upon each other,
so that the violet would be by the side of the central bright band.
Observation proves this. Thus, by this memorable experiment
the truth of the undulatory theory is confirmed; mathematical
analysis has also drawn from it a crowd of inferences, some
already known by observation, others outstripping observation and
serving as a guide to it. The names of Huyghens, Young, and
Fresnel will remain for ever attached to this beautiful theory, as is
that of Newton to the theory of universal gravitation.

Let us now return to the phenomena of diffraction, all of
which flow from this principle of interference of luminous waves.
They are so numerous that we can only choose some of the most
remarkable.

Newton, while repeating and varying Grimaldi's experiments on
the enlarged shadows of fine bodies, such as hairs, thread, pins, and
straws, became convinced that the deviation of the luminous rays was

F F

362 PHYSICAL PHENOMENA. [BOOK in.

not due, as was at first believed, to a refraction in a thin stratum of
denser air surrounding the bodies. He saw also that the formation
of fringes did not depend on the nature of the substances used.
Whether metals, stones, glass, wood, or ice, &c. were used, he
always recognised three fringes succeeding each other and starting
from the shadow. The interior fringe was violet, deep blue, light
blue, green, yellow, and red; the exterior one, pale blue, pale
yellow, and red. He also observed that monochromatic lights
produce fringes of unequal width. But all his experiments led
him to the conclusion, that the rays of light undergo, in passing
by the edges of a body, inflections which are stronger the nearer
they graze the surface. This was a natural hypothesis, in accord-
ance with the . emissive theory ; but we shall presently understand
the true explanation.

The very numerous experiments which have been since performed
in connection with this subject may be arranged under two heads.
The first comprises phenomena of diffraction produced by rectilinear
edges ; for instance, by one or by several very narrow slits, in the
form of parallelograms, or by a very fine screen, a metallic thread,
or a hair : the second comprises phenomena obtained when the
diffraction is produced by means of one or more extremely small
apertures, either square, triangular, circular, or by the edge of a
circular screen of small dimensions. Of the systems of fringes pro-
duced under these varied circumstances, some are coloured, proceeding
from white light ; others, monochromatic, from light of a single colour,
— for instance, red light. We see, in many cases, fringes accompanied
by a multitude of small spectra like the rainbow, the bright colours
of which add to the beauty of the phenomenon.

Sir J. Herschel observed curious diffraction effects by placing
in front of the object-glass of an astronomical telescope diaphragms
of different forms, and then observing single and double stars. With
an annular opening, he saw coloured rings surrounding the images
of luminous points, which then presented discs similar to those of
the planets. Triangular diaphragms gave, on the contrary, stars
with six rays ; an aperture formed by twelve concentric squares
gave a star with four rays. Lastly, by piercing in a regular manner
equilateral triangles on the diaphragm, he obtained a series of cir-
cular discs, arranged on six lines, on which they diverged, starting

cu AP. xni.] INTERFERENCE OF LUMINOUS WAVES. 363

from a central colourless and very bright disc; they were, more-
over, each surrounded by a ring more or less coloured, and spread
into spectra as they extended farther from the centre.

These phenomena are of great interest; the magnificent colours
which are presented to the eye form, as it were, so many pictures,
the variety of which equals their splendour. But to the eyes of the
physicist they present still greater interest, inasmuch as they are
so many confirmations of the beautiful theory of the undulations of
the ether. Mathematical analysis applied to the different phenomena
of diffraction produces results which agree, in a marvellous manner,
with those -of observation. We have already said that they some-
times outstrip it, and of this the following is a remarkable example.

Fid. 247.— Effects of diffraction in telescopes. (Sir J. Herschel.)

The geometer Poisson, having submitted to calculation the problem
which has for its object the determination of the nature of the
shadow and the fringes produced by an extremely small opaque
disc exposed to the light which diverges from a luminous point,
found that the centre of the shadow ought to be as brilliant as if
the disc did not exist : this light was an effect resulting from the
diffraction of luminous waves on the edge of the screen. Such a
result was so opposite to preceding observations, that Poisson pre-
sented it as a serious objection to the undulatory theory. But Arago
having made the experiment with requisite care, by using a very small
metal disc cemented on a diaphanous and perfectly homogeneous

F F 2

3G4 PHYSICAL PHENOMENA. [BOOK ITT.

glass plate, found that the luminous point appeared as calculation
had indicated. It was as if the shadow was produced by a screen
pierced at the centre. This experiment evidently affords one of
the most beautiful triumphs of the theory, — a decisive proof in
favour of the undulatory theory of light and of the existence of
the ether.

Fraunhofer, whose beautiful experiments on the lines of the
spectrum we have already described, introduced into the study of the
phenomena of diffraction the excessive precision which so eminently
distinguished him. After having observed the images produced by a
very limited number of small openings, he conceived the idea of
examining the effect produced when light traverses a grating formed
of a multitude of very fine threads either parallel or crossed. He
first used a grating of brass wire, composed of numerous very fine
wires, stretched on a rectangular frame by means of screws suitably
arranged. Then, to obtain a greater regularity and delicacy in the
intervals through which the light passed, he traced parallel and equi-
distant lines on plates of glass covered with gold leaf; then engraved
them with diamonds on the glass itself, thus forming more than
1,000 divisions per millimetre. Each of the striae is an opaque
screen, and the interstices left by the striae allow the light to
pass through. However, a much smaller number of divisions makes
the grating more regular, as it is almost impossible to secure that the
thickness of the lines or intervals between them shall be even
approximately constant in the finer gratings, and thirty- eight lines in
a millimetre, 1,000 per inch, are sufficient to show the phenomena.

Beside the parallel-line grating, Fraunhofer studied gratings with
square meshes, formed by two series of lines crossing each other at
right angles ; also those of circular and other forms of mesh. In
this manner he obtained a number of figures, in which the fringes and
spectra are distributed with wonderful symmetry ; but he did more?
he studied the laws of this distribution — laws which M. Babinet has
proved to be necessary consequences of the principles of interference.

The following are the phenomena resulting from the passage of
light through a grating with parallel lines : at the centre is a bright
line, then two rich dark intervals followed on each side by two
spectra — the violet of which is nearest the centre, and so pure that
the dark lines are easily distinguished. Beyond this there are two

CHAP, xiii.] INTERFERENCE OF LUMINOUS WAVES. 365

fresh dark bands ; and lastly, two series of superposed spectra, paler
and more and more extended. A grating with square meshes gives
us, besides the bright central line and two series of spectra more
extended than those of the grating with parallel meshes, in the
four right angles a multitude of small spectra radiating towards the
centre. Newton had a glimpse of the phenomena of diffraction
through small apertures and gratings, as the following passage in his
" Optics " shows : " On looking at the sun through a piece of black
ribbon held close to the eyes, we perceive several rainbows ; because
the shadows which the fibres or threads throw on the retina are
edged like coloured fringes." A beautiful effect is produced by the
diffraction of solar light through the grating formed by the broad
part of a bird's feather. Fringes of a like nature can be equally
observed by the light of a candle, with the eyes nearly closed, the
lashes, on joining, forming meshes of irregular form.

It is by the interference of luminous rays that physicists ex-
plain the bright colours which
are noticed on certain bodies
whose surfaces are covered with a
multitude of very fine striae : the
feathers of several birds, and the
surface of mother-of-pearl, for in-
stance, are formed of numerous
striae which reflect all the pris,
matic colours. Sir David
Brewster, having occasion to fix
mother-of-pearl to a goniometer
with a cement of resin and wax,
was greatly surprised to see the
surface of the wax bright with the

prismatic colour of the pearl : he repeated the experiment with dif-
ferent substances, — realgar, fusible metals, lead, tin, isinglass, — and in
each case he saw the same colours appear. An Englishman, Mr.
John Barton, applied this property of striated surfaces to the arts ;
he worked very fine facets on steel buttons and other objects which,
in the light of the sun, gas, or candles, exhibit designs brilliant
with all the colours of the spectrum. " These colours," says Brewster,
" are scarcely surpassed by the fire of the diamond."

366 PHYSICAL PHENOMENA. [BOOK in.

The following is another phenomenon which seems to belong to
the phenomena of interference, as it is explained by M. Babinet ;
the description of which we take from the account given by the
observer, M. A. Necker : —

" To enjoy the sight of this phenomenon/' he says, " the observer
should stand at the foot of a hill, interposed between himself and the
spot where the sun sets and rises. He is then completely in the
shade ; the upper edge of the hill or mountain is covered with woods,
trees, or detached bushes, which appear black against a perfectly
clear and bright sky, except at the place where the sun is on the
point to appear or disappear. There the whole of the trees and
bushes which crown the summit — branches, leaves, trunks, &c. —
appear with a bright and pure white, and shine with a dazzling light
although projected on a background, which is itself luminous and
bright as the part of the sky near the sun always is. The smallest
details of the leaves and little branches are preserved in all their
delicacy ; and it might be said that the trees and forests are made of
the purest silver, with all the art of the most skilled workman. Swal-
lows and other birds, which fly across this region, appear as sparks
of dazzling whiteness."

To those who know how to observe, Nature has a magnificence
which the skill of the most ingenious experimenter can never ap-
proach. That which makes the merit of the inquirer is not so much
to reproduce her — to multiply the phenomena, the pictures of which
she shows us — as by dint of patience, sagacity, and genius, to discover
the reasons of things and the laws of their manifestations. From
this point of view, natural philosophy is one of the grandest studies
which the human mind can pursue.

CHAP, xiv.] COLOURS OF THIN PLATES. 367

CHAPTER XIV.

COLOURS OF THIN PLATES.

The soap-bubble — Iridescent colours in thin plates — Newton's experiment on
coloured rings ; bright and dark rings — Laws of diameters and thicknesses-
Coloured rings are phenomena of interference — Analysis of the colours of the
soap-bubble.

THE most beautiful and brilliant phenomena are not always
those which require the most costly and complicated instru-
ments to produce them. Who among us, in his childhood, has not
amused himself, with a pipe or straw and soap and water, in
blowing and throwing into the air bubbles of the most perfect
form and the most delicate and varied colours ?

At first, when the sphere of the bubble is of small diameter,
the pellicle is colourless and transparent. By degrees, the air
which is blown into the interior, pressing equally on all parts of
the concave surface, increases the diameter while it diminishes
the thickness of the envelope; it- is then that we see the appear-
ance, at first feeble and then brighter, of a series of colours arising
one after the other, and forming by their mixture a multitude of
iridescent tints, until the bubble, diminished in thickness, can no
longer offer sufficient resistance to the pressure of the gas which
it incloses. Black spots then present themselves at the top, and
soon the bubble bursts. It is always at the upper portion of the
liquid sphere that the black spots which announce its disappearance
may be observed.

This simple experiment and childish recreation, which offers so
much attraction to the eye of the lover of colours, is not less
beautiful or interesting to the man of science. Newton made
it the object of his studies and meditations, and, since the time

368 PHYSICAL PHENOMENA. [BOOK in.

of this great man, the colours of the soap-bubble hold a legitimate
place among the most curious of optical phenomena. Moreover,
this is one particular instance of a whole series of phenomena,
observed whenever light is successively reflected and refracted by
surfaces which bound thin plates of transparent bodies. Solids,
liquids, and gases are equally suitable for this kind of experiment.
Crystals which can be reduced to very fine laminae by cleavage, like
mica, gypsum, talc, glass blown into extremely thin bulbs, the
surface of annealed steel which retains a thin, coating of oxide, show
iridescent colours similar to those of a soap-bubble. The bright
shades which ornament the membranous wings of dragon-flies,
those seen on pieces of glass after exposure to damp, and on the
surface of oily water, belong to the same series of phenomena.
They are studied in physics under the common denomination of the
colours of thin plates.

Before speaking of the cause of this decomposition of light into
its constituent colours, we will endeavour to give an idea of the
conditions under which it is produced, and the laws which govern
the succession of tints, at first sight so changeable and mobile. Let
us follow Newton in his celebrated experiments.

The starting-point of this great physicist was the following
observation. He says, in his " Optics," that " having pressed two
prisms strongly together, so that their sides touched each other
(which were perhaps very slightly convex), I perceived that the
place where they were in contact became quite transparent, as if
there had been here only a single piece of glass. For, when the
light fell on the air comprised between the two prisms so obliquely
that it was totally reflected, it appeared that at the place of contact
it was entirely transmitted. Looking at this point, a black and
obscure spot was seen, like a hole, through which objects placed
beyond it would distinctly appear."

Newton, having turned the prisms round their common axis, saw
the gradual appearance around the transparent spot of a series of
rings alternately bright and obscure, and coloured with different
tints. To account better for the production of these rings, he used
two glasses, one plano-convex, the other convex on both sides;
and both of great radius of curvature. He then placed one over
the other, and pressed the convex side gently on the plane side;

CHAP. XIV.]

COLOUES OF THIN PLATES.

369

in this position the two glasses had between them, around the
central point of contact, a layer of air, — a very thin meniscus, the

•.ssniaiiiiB

Fio. 249.— Thin plate of air comprised between two glasses, one plane, the other convex.
(Newton's experiment of coloured rings.)

thickness of which, at the centre nil, continued to increase imper-
ceptibly. The following are the phenomena which he observed : —
Eeceiving the reflected light in a direction nearly normal to
the plane surface of the layer of air, he saw around the central

Fio. 250. — Newton s coloured rings.

point of contact a series of differently coloured concentric rings
becoming narrower as they were further from the centre. Each
colour appeared, at first, as a circle of uniform tint, which circle

370 PHYSICAL PHENOMENA. [BOOK m.

expanded as the pressure on the upper glass was increased, until a
new colour issuing from the centre transformed it into a coloured
ring. Lastly, at the centre itself, there appeared a black spot.

The following is the order and colour of the rings represented
in Fig. 250. The colours indicated start from the centre 0 :—

From o to A, black, blue, white, yellow, red ;

„ A „ B, violet, blue, green, yellow, red ;

„ B „ c, purple, blue, green, yellow, red ;

„ c „ D, green, red ;

„ D „ E, greenish blue, red ;

„ E „ F, greenish blue, pale red ;

„ F „ G, greenish blue, reddish white.

If, instead of receiving the light reflected on the two surfaces
of the thin plate, we look at ordinary light through a system of two
similar lenses, a series of coloured rings will be seen, but their
colours will be feebler than those of the rings seen by reflection.
Moreover, the order of the colours is entirely different, and, instead
of a black spot at the centre, a white spot is seen. The following
is the series of the various tints forming the coloured rings seen
by transmission : —

White, red-yellow, black, violet, blue ;
White, yellow-red, violet, blue ;
Green, yellow-red, green-blue, red j
Bluish green ;
Ked, bluish green ;
Bed.

If we compare this second series with the first, we see that
the tints which occupy the same order in the two systems of
rings are precisely complementary, so that the transmitted light
and the reflected light at any one point of the layer of air
produce white light when re-united. This consequence of the
two experiments has been verified by Young and Arago, who,
having placed the two glasses in such a manner as to cause both
the reflected and transmitted lights to reach the eye with the
same intensity, saw the rings disappear.

In order to observe the rings, Newton used the various simple
colours of the spectrum. In this instance he perceived, by reflec-
tion, rings which were alternately black and bright, — the latter

CHAP, xiv.] COLOURS OF THIN PLATES. 371

presenting the tint of the simple colour used. But the diameters
of the rings varied in size, according to the colour of the light,
and they widened on passing from the violet to the red.
We can therefore understand how it is that the rings obtained
with white light are iridescent. The different colours of which
white light is formed, produce each its series of rings ; but as
the dimensions are different, the superposition is not exact; the
dark rings disappear because they are again covered by other shades
of light, except at the centre, and only when these shades are
blended together in a proper proportion does the one ring of
white light before observed appear. When we introduce water be-
tween the glasses, the rings are still visible, but they are smaller
and narrower, and the tints are fainter. Lastly, if, instead of a
gaseous or liquid medium, the space between the two glasses is a
vacuum, coloured rings are still seen, showing no perceptible difference
from those given by air.

Newton, with his accustomed sagacity and precision, could not
confine himself to the proving of these facts and others into the
details of which we cannot enter here ; he sought out the law of the
production of the rings, and thus he succeeded in tracing to the same
principle the different phenomena described at the commencement
of this chapter, — the iridescent colours of soap-bubbles and thin
plates in all solid, liquid, and gaseous masses. He carefully
measured the diameters of the successive rings obtained with mono-
chromatic light, at the moment when the black spot of the centre in-
dicated that the surfaces were in contact. From it he deduced the
geometrical ratios, which gave the relation of the diameters to the
thicknesses of the thin plate, and these thicknesses themselves ; and
he determined the following laws : —

The squares of the diameters of the bright rings, seen by reflection,
are related in the ratio of the odd numbers, 1, 3, 5, 7, 9.

The squares of the diameters of the dark rings are as the even
numbers, 2, 4, 6, 8.

In regard to the rings seen by transmission, as they occupy pre-
cisely inverse positions, each obscure ring being replaced by a bright
ring, and each of those by a dark ring, their diameters evidently
follow the same laws, and the series of numbers is inverted.

So much for the relative dimensions of the bright and dark rings.

372 PHYSICAL PHENOMENA. [BOOK m.

As to the thicknesses of the layer of air interposed between the
glasses, they continue to increase from the centre towards the extremi-
ties ; but we find that the values which correspond to the rings of
the different orders are odd numbers for luminous rings, and even
numbers for black or obscure rings.

These laws, although so simple, are general. . Newton concluded
that the phenomenon of coloured rings depends on the variable
thickness of the thin plate interposed between the two surfaces, and
the nature of the substance of which it is composed, but not at all on
that of the glasses between which it is interposed. He endeavoured
to connect it with the emission theory of light, supposing that the
luminous rays, on being propagated, undergo periodical changes —
"fits of easy transmission arid easy reflection" — which sometimes
render them apt to be reflected and sometimes apt to be transmitted !
In the present day, as the undulatory theory is admitted, the coloured
rings are explained in a simpler way on the principle of interference.
A ray of light which penetrates to the first surface of the plate is
partly reflected and partly transmitted; transmitted as far as the
second surface, where it is again reflected. The two rays, thus
reflected on each surface, interfere, as we have already seen, and the
luminous effect is destroyed or augmented according as the delay
of the second equals an odd number of half-lengths of wave, or
an even number of these same lengths. Hence, darkness in the first
case, and light in the second, or, in other words, dark rings and bright
rings.

Analysis applied to this interesting case of the undulatory theory
also proves the laws of the diameters and thicknesses, which Newton
first discovered by experiment. As the lengths of the waves vary
according to the nature of the simple light, and diminish in passing
from red to violet, we see that the rings of this latter colour must
be narrower than the red rings. Now, in what way is this theory
applicable to the phenomenon of the soap-bubble colours, colours so
variable and changing, and which are continually mixed and blended
with each other ?

Newton showed the identity of the coloured rings obtained by
means of glasses, and those which appear on bubbles. To study
these, he took the precaution of protecting the blown soap-bubble
from the influence of the external air, which, earning the thickness

CHAP. XIV.]

COLOURS OF THIN PLATES.

373

to vary irregularly, changes the colours one into the other, and

thus prevents them from being exactly observed. He says, "As

soon as I had blown one, I covered it with a very transparent

glass; and by this means

its different colours ap-

peared in regular order, like

so many concentric rings

surrounding the top of the

bubble." When these pre-

cautions are taken, the

coloured rings visible at

the top of the bubble are

seen slowly spreading out,

in, proportion as the flow

of the water towards the

bottom of the liquid sphere

renders this thinner, and,

after having descended to

the base, each disappears in

its turn. Fig. 251 shows

the disposition of these

coloured bands.

The phenomenon thus
regulated loses its beauty
from an artistic point of
view, but in the scientific
it gains in interest
Usually the zones of several rings can be seen, in spite of the irregu-
larity of colour and their mixture. By degrees, the bubble becomes
so thin at the top that the black spot makes its appearance, often
mixed with smaller and darker spots ; and almost immediately
afterwards the bubble bursts and disappears.

According to Newton, the following is the exact order in which
the coloured rings succeed each other from the first coloration of the
bubble until its disappearance : — Eed, blue ; red, blue ; red, blue ; red,
green ; red, yellow, green, purple ; red, yellow, green, blue, violet ; red,
yellow, white, blue, black.

Now, if we compare this series with that of the coloured rings

Fia 251>~ Colours of thin plates m

374 PHYSICAL PHENOMENA. [BOOK m.

obtained by means of the two glass surfaces in the first experi-
ment, it will be noticed that they are arranged exactly in the
opposite order, and this is as it should be, if the same cause pro-
duces both these effects. At the commencement the bubble is
too thick for the appearance of colours; it is colourless. Then its
thickness diminishes more and more, so that at last the black
corresponding to the least thickness appears exactly like the black
spot of the first ring, which is found at the point where the two
glass surfaces are in contact. This refers to colours seen by
reflection. The bubble, once formed, ought to be observed in such
a manner that it can reflect towards the eye the light of a whitish
sky ; and, in order better to distinguish the rings and colours, a
black ground should be placed behind it. But the soap-bubble
may also be observed by looking at ordinary light through it.
Coloured rings are again formed ; but they are of small bril-
liancy, and their successive colours are complementary to those
given by reflected light. It is easy to assure oneself of this fact.
If we examine the bubble by the light of clouds reflected to the
eye, the colour of its circumference is red; at the same instant,
another observer, looking at the clouds through the bubble, will find
that its circumference is blue. On the other hand, if the contour of
the bubble is blue by reflected light, it appears red by transmitted
light.

Now, it is easy to understand why the soap-bubble, observed in
the open air, presents in the iridescent colours of its surface that
irregularity, that mobility, that perpetual mixture of tints which
causes it to be one of the most beautiful phenomena due to the
decomposition of light by interference. The agitation of the air
around the bubble, added to the want of homogeneity in the soapy
water in different parts, and to the evaporation which takes place
in a very unequal manner, produces numerous currents in the
liquid pellicle, which, opposing the action of gravity in every
direction, prevent the water from descending by regular zones
towards the base of the bubble. Its thickness thus varies from
one point to another, and, as it is on this thickness that the
production of the different tints depends, these are distributed in
the most varied manner. On the other hand, in a closed flask
the air being saturated with vapour, evaporation and the agitation

CHAP, xiv.] COLOURS OF THIN PLATES. 375

due to the external air no longer exist, and the rings appear with the
regularity indicated by calculation.

We have forgotten to mention that the laws discovered by Newton
regarding rings furnish a means of calculating the thickness of the
liquid film of any given colour. At the point where the black spots
are situated this thickness is the least ; and it is then about the two
hundred and fifty-thousandth .part of an inch. . Hence it follows that,
if one could produce a soap-bubble uniformly of this thickness, it
would be completely invisible.

376 PHYSICAL PHENOMENA. [BOOK in.

CHAPTER XV.

DOUBLE REFRACTION OF LIGHT.

T71 RASMUS BARTHOLIN, a learned Danish doctor, who lived at
J-J Copenhagen towards the middle of the seventeenth century, on
examining some crystals which one of his friends had brought him
from Iceland, was surprised to observe that objects appeared double
when seen through them. He noticed this singular phenomenon in
1669, and described the circumstances of the case in a special memoir.
Twenty years later, Huyghens undertook the study of what has since
been called double refraction ; he determined its laws, and propounded
a theory in accordance with the principles of the undulatory theory
of which he had laid the foundations.

Since Bartholin's discovery and Huyghens* observations, these
phenomena have been studied in all their phases, and the whole
now constitutes an entire branch of optics. Before describing the
principles of these phenomena, we will call to mind what happens
when a beam of light falls on the surface of a transparent medium
like water or glass. On reaching the surface, part of the luminous
beam is reflected regularly, so as to give an image of the object ;
another portion is reflected irregularly in all directions. Thus part
of the light returns on its path. The other portion of the ray
penetrates into the transparent substance, where it is propa-
gated without altering its direction, if the incidence is normal;
whereas it is refracted, if the ray falls obliquely on the

CHAP, xv.] DOUBLE REFRACTION OF LIGHT. 377

surface. In both cases the ray generally remains simple ; it is still
simple when it emerges from a transparent medium, so that the eye
which receives it only sees a single image of the luminous source.
This, however, is by no means always the case ; certain substances
act upon a ray of light in its passage through them and split it up
into two, whence two images of the object, instead of one, are seen,
as Bartholiri first proved.

In lodes and metamorphic limestones and clays, a mineral is
found which crystallizes in the form of a solid rhombohedron with
six parallel sides, which is very transparent arid colourless; its
chemical composition shows it to be a carbonate of lime with traces
of protoxide of manganese. The most beautiful specimens come
from Iceland, and attain a thickness of several inches ; the mineral
is known under the name of Iceland spar.

FIG. 252.— Specimen of Iceland spar.

Crystals of this kind are split with the greatest ease in certain
directions, so that an exact geometrical form can be given them,
which is more convenient for the study of their optical properties.
The rhombohedron is then bounded by six lozenges equal among
themselves.

Each of these lozenges has two obtuse angles, measuring 101° 55',
and two acute angles of 78° 5'. Of the eight solid angles which form
the summits of the crystal, six a-re formed of an obtuse angle and
two acute angles ; the two others, of three obtuse angles.

Let us imagine that these two latter are joined by a straight line :
this diagonal of the rhombohedron is of great importance in reference

G G

378 PHYSICAL PHENOMENA. [BOOK in.

to the phenomena of which we are about to speak ; this is called —
we shall presently see why — the optic axis of the crystal.

We will now describe the phenomena of double refraction, which
can be easily observed by means of a specimen of Iceland spar.

Let us take a piece of this crystal ; place it on a line of writing,
and look through it: we witness the phenomenon which struck
BarthoKn. Each letter is doubled. Let us, also, notice that each
separate image is not so black as the letter itself : it has a greyish
tint, and that this has nothing to do with the absorption of light by
the crystal is evident, because the tint is black where the two images
are superposed. The edges of the crystal itself seen by refraction
appear double ; and a straight line traced on paper is changed into
two parallel lines. If we allow a beam of solar light to fall on one of
its sides, the luminous ray issues as a double ray and forms two sepa-
rate images on a screen, the distance between them depending on the
inclination of the incident ray to the side of the crystal. We will

FIG 253.— Double images of objects seen through a crystal of Iceland spar.

now go farther into the analysis of the phenomenon ; and to simplify
the experiment, let us examine one part at a time. Seen through the
crystal, the images appear double ; but if we turn the crystal on
itself, parallel to the faces of incidence and emergence, we observe
that one of the images turns round the other, and when an entire
revolution has been described by the crystal, one image returns to
its first position, after having described a circle round the other
immovable one. When, instead of observing one point, the same
experiment is made on a straight line, it will be noticed that in
two different positions of the crystal one of the lines, which appears
to be moved parallel to the other, attains a maximum digression ;
in two other positions, the two images seem to coincide. But this
coincidence is only apparent; for if a point on the observed line

CHAP, xv.] DOUBLE REFRACTION OF LIGHT. 379

is marked, we see the double image of this point, where the
images of the lines are superposed. In fact, the one line has
been slid along the other. Thus the rotation of one of the images
round the other takes place in this case, as in the preceding one.
Let us now see why the name of ordinary image is given to the
immovable image, and that of extraordinary image to that which
rotates round the first. The reason is, that the refracted ray which
produces the immovable image follows during its path the laws
of simple refraction, such as they were enunciated by Snellius and
Descartes, whilst the other ray does not obey the same laws.1 This
characteristic difference between the two images can be exhibited in
many ways. If we cause a ray of light to fall perpendicularly on
one of the faces of the crystal, it will be bifurcated in penetrating
into the interior; but one of the rays will follow the direction of
the incident ray, and will not be refracted on its emergence : this is
the ordinary ray, which obeys Descartes' law. The other ray will
be deviated from the direction of the incident ray, both on its
entrance into and its emergence from the crystal : this is the ray
which produces the extraordinary image.

When the incidence is oblique, the two rays are refracted ; but the
ordinary ray is equally deviated whatever the position of the crystal
may be, provided that the lines of incidence and emergence remain
parallel to their first position ; in a word, its path is that which it
would preserve through a piece of glass with parallel sides. It is not
so with the other ray, which gives rise to the extraordinary image,
since this image, as we have already shown, turns round the first, if
the crystal be caused to revolve parallel to itself.

In this movement of the extraordinary image there is a circumstance
which must be noted. If the crystal be placed on a sheet of paper on
which a point is marked, and the eye be in the plane of incidence, the
ordinary refracted ray will be also in this plane, as the law of simple
refraction shows, and the ordinary image 0 of the point will be on the
line 1 1 of the plane of incidence with the paper (Fig. 254). But it will
not be the same with the extraordinary image E, and the lines which
join the two images 0 E will make an angle with the line of which

1 In a word, on the one hand, the extraordinary refracted ray is not generally in
the plane of incidence ; and, on the other, the relations of the sines of the angles
of incidence and refraction do not remain constant.

G G 2

880

PHYSICAL PHENOMENA.

[BOOK HI.

we Lave spoken. Now, we observe that this line o E always remains
parallel, during the rotation movement, to the bisector A D of the
obtuse angle of the side parallel to the plane of the paper. Also
when, owing to this movement, this bisector is placed parallel to I I,
the extraordinary image is itself on this line, and the two refracted
rays are both in the plane of incidence.

FIG. 254. — Positions of the extraordinary image in relation 1o the plane of incidence.
Principal section.

There is then, among the sections which cut the crystal perpen-
dicularly to one of its sides, a section of such a nature that if the
incident ray were found contained there, the extraordinary ray would
obey the first law of simple refraction exactly like the other ray.
This plane is called the principal section. Each plane, perpendicular

FIG. 255. — Principal sections and optic axis of Iceland .spar.

to one of the faces of Iceland spar, and parallel to the small diagonal
of the lozenge, or to the bisector of the obtuse angle, is one principal
section of this face.

Each principal section is parallel to the optic axis, and this
condition suffices ; so that if an artificial face were cut in the

CHAP, xv.j

DOUBLE REFRACTION OF LIGHT.

381

crystal, any plane perpendicular to this face and parallel to the
optic axis, would also be a principal section of the artificial face.
Lastly, if we make an artificial face ABC perpendicular to the optic
axis N I, every ray which falls on this face will necessarily be in
a principal section, and the two refracted rays will always be in the
plane of incidence. In this case
observation proves that if the inci-
dent ray is normal to the artificial
face, the refracted ray alone remains.
This is therefore a direction in
which the phenomenon of bifurca-
tion vanishes: double refraction no
longer takes place, when the inci-
dent Tay is parallel to the optic axis.
Monge made a remarkable ex-
periment, very easy to repeat,
which shows us the path followed by the rays emanating from a
luminous point through the crystal in giving rise to the two images,
ordinary and extraordinary, of the point. If we examine the double

FIG. 256. — Artificial section ]>erpeiidiciuar
to the optic axis.

Fio. 257.— Crossing of the rays which produce the ordinary and extraordinary. image.

image of a point s (Fig. 257), situated at some distance from the
lower face, and place underneath this face an opaque card, a b, which
we slide along from I towards a, we shall notice with surprise that

382 PHYSICAL PHENOMENA. [BOOK in.

the most distant image of the point first disappears; and this is
explained as follows. A luminous incident pencil, s I, is bifurcated
and gives two refracted rays; whence on issuing from the parallel
face, two emergent rays arise; they diverge, and one of them can
then only penetrate the eye : let us suppose this the one which
produces the ordinary image o. An incident pencil, near the first,
will also give two emergent rays, one of which will penetrate to
the eye and will produce the extraordinary image E. As the faces
of the crystal are parallel, each emerging ray is composed of rays
parallel to those of the incident ray. As those which produce
the image are concentrated in the eye, it is necessary that the
corresponding refracted rays should cross each other in the crystal.

Monge's experiment is explained thus : the card a b first inter-
cepts the pencil which produces the most distant image, and it is
this — the extraordinary image E — which must naturally disappear
first. '•; V

Such are the most remarkable circumstances which constitute
the phenomenon of double refraction. The laws which govern this
phenomenon are too complex to allow us to explain them in an
elementary work like this. But we will endeavour to give, in a
few lines, some idea of the difference which exists between simple
and double refraction.

We have already said that the ordinary ray follows the two laws
of Descartes ; in other words, that the refracted ray is always in the
plane of incidence, and that if the angle of incidence is changed,
the relation which exists between its sines and those of the refracting
angle is always constant. The extraordinary ray only follows the
first of these laws, if the incident ray is in a principal plane. But
it does not follow the second, so that the relation of the sines, which
is called the index of refraction, varies according to the angle that
the incident ray makes with the optical axis of the crystal. Is this
angle nil, or is the incident ray parallel to the optical axis ? In this
case only, double refraction disappears ; one of the images is blended
with the other : there is equality between the ordinary and extra-
ordinary indices of refraction.

As the angle increases, so does the inequality of these indices, and
it is a maximum if the incident ray is perpendicular to the optic
axis. For Iceland spar, the only crystal endowed with the power

CHAP, xvi] DOUBLE REFRACTION OF LIGHT. 383

of double refraction that we have hitherto examined, the index of
refraction of the ordinary ray is greater than that of the extra-
' ordinary ray. The contrary takes place, if certain other bi-refractive
substances are employed, such as rock-crystal. In order to explain
the cause of this difference we should be obliged to expound the entire
theory of simple and double refraction, according to the undulatory
theory, to show that refraction is caused by the difference of velocity
which the ether waves undergo in passing from one medium into a
more refractive one ; that the ordinary ray acts as if it were in a
homogeneous, non-crystallized medium, whilst the extraordinary ray
is propagated with more or less facility, according as it is moved in
such or such direction relatively to the
position of the crystalline molecules.

In Iceland spar, the velocity of the
extraordinary ray is the greatest ; and
the reverse is the case in rock-crystal.
Hence the names oi -positive and negative
crystals have been given to substances
which possess double refraction according
as they are included in one or the other
category, the type being for the first, rock-
crystal, and for the second, Iceland spar.
Tourmaline, rubies, emeralds are nega-
tive crystals like Iceland spar ; quartz —
the mineralogical name of rock-crystal
— sulphate of potassium and of iron,
hyposulphate of lime, and ice are FIG. 258.-Roek-crj.tui.

numbered with the positive crystals. Double refraction is also pro-
duced in a certain class of crystalline substances known under
the name of crystals with two axes, or biaxial crystals. Topaz,
arragonite, sulphate of lime, talc, feldspar, pearl, and sugar are
crystals with two axes : in each crystal of this kind there are two
different directions in which the incident ray passes without being
bifurcated; these two directions are the optic axes of the crystal.
But there is an essential difference between the phenomena of double
refraction • in crystals with one axis, or uniaxial crystals, and those
of crystals with two axes, or biaxial crystals. In the first, one of
the two refracted rays follows the laws of simple refraction : in

384 PHYSICAL PHENOMENA. [BOOK in.

the others, the two rays are both extraordinary : neither of them
follows Descartes' laws. Fresnel's experiment proves the fact very
simply. A topaz is divided into several pieces cut in different
directions, and these pieces are fastened together by their plane
surfaces so that the form of a parallelopiped is given to the whole.
Then on looking at a straight line, two images of the line are seen,
and each of these images is a broken line of which the different
portions correspond to the fragments of the topaz : now, if one of
the systems of refracted rays followed Descartes' law, the image
produced would be a straight line, for the direction of the rays in
the prism would then be independent of the direction of the optic
axis in each piece which composes it. Experiment thus proves
that the two rays are both extraordinary rays. We shall soon find
another means of distinguishing crystals with one or two axes from
each other.

We may conveniently end this chapter by enumerating the
refractive media in which phenomena of this order are not mani-
fested, or, iii other words, which are endowed with simple refraction.
First there are gases, vapours, and liquids ; then, among substances
which have passed from a liquid to a solid state, those whose mole-
cules have not taken a regular crystalline form, such as glass, glue,
gum, and resins ; lastly, crystals whose primitive form is the cube,
the regular octahedron, and the rhomboidal dodecahedron. It must
be added that the bodies belonging to these two last categories can
acquire the property of double refraction when they are subjected
to violent compression or expansion ; also when their different parts
are unequally heated. Certain solids belonging to the vegetable
or animal kingdom, — horn, feather, and mother-of-pearl, — are also
endowed with double refraction.

CHAP, xvi.] POLARIZATION OF LIGHT. 385

CHAPTER XVI.

POLARIZATION OF LIGHT.

Equal intensity of the ordinary and extraordinary images in a double refracting
crystal — Natural light — Huyghens' experiments ; variations of intensity with
four images ; polarized light — Polarization of the ordinary ray ; polarization of
the extraordinary ray : the two planes in which these polarizations take place
— Polarization by reflection.

WHEN a luminous object is viewed through a double refracting
crystal, a rhombohedron of Iceland spar for instance, we know
that two distinct images are seen ; one ordinary, following the law
of simple refraction, the other extraordinary, the properties of which
we have indicated in the preceding chapter. The latter is easily
recognised as it revolves round the other, when the crystal is made
to rotate in a plane parallel to the faces of incidence and emergence
of the rays. It is now necessary to remark that, in all these posi-
tions, the relative intensity of the two images has not varied : the
brightness of each of them is the half of that of the luminous object,
as can be easily proved by direct observation. Let us suppose that
we examine a small white circle on a black ground. In all parts
where they are separated, the two images, ordinary and extraordinary,
of the circle present a greyish tint of the same intensity, and the
brightness equals that of the object when the two images are super-
posed. Indeed, the same phenomenon always takes place, whatever
the respective colours of the object and ground may be. The same
result is also shown if we allow a ray of solar light to fall on the
crystal and receive the two refracted rays on a converging lens, the
two images being projected on a screen (Fig. 259). If the crystal
is made to revolve parallel to the face of incidence, the two images
are displaced, each describing a circumference of a circle, and we

386

PHYSICAL PHENOMENA.

[BOOK in.

observe that in every position the luminous intensities are equal.
If the two images are partly superposed, the brightness of the super-
posed parts will be double that possessed by the separate parts, as
shown in Fig. 260.

FIG 259. — Propagation of ordinary ami extraordinary images of a double refracting crystal.

Equal intensity.

An old and beautiful experiment, due to Huyghens, proves that
the rays which emerge from Iceland spar have acquired new and
remarkable properties after their deviation in the crystalline medium,
— properties which they did not possess before passing through the

crystal. This experiment consists
in receiving the ordinary and
extraordinary rays, after their
emergence from the first rhombo-
hedron, on a second crystal, and
examining the relative intensities
of the images which they produce,
when the second crystal is caused
to revolve over the first. The
following is a very simple method
of observing the phenomena which
are thus produced; it is that
which Huyghens himself devised.
Let us place the first ciystal on a

black spot on a white ground ; there will be two images of equal in-
tensity. We will now place a second piece of Iceland spar on the first,
and it must be placed so that their principal sections coincide; in order
that this condition may be realized, the faces of one must be placed
parallel to the faces of the other: there will be only two images of the

FIG. 260.— Equal intensity of ordinary
and extraordinary images.

CHAP, xvi.] POLARIZATION OF LIGHT. 387

same intensity as before. Only, the two images, ordinary and extra-
ordinary, will be more separated than by one crystal. The same effect
would take place if the principal sections of the two rhombohedra
remained in the same plane, or in parallel planes when even the two
opposite faces of the crystals were not parallel ; and it is not necessary
that, in the first position, the two rhombohedra should touch each
other.

We observe then, already, a difference between the luminous ray
before its refraction by Iceland spar, and each emerging ordinary or
extraordinary ray ; whilst the first is bifurcated in penetrating the
crystal, it appears that the two others remain simple in penetrating
a second crystal.

Fis. 261.— Huyghens' experiment. Variations in intensity of the images seen when one prism of
Iceland spar is rotated over another.

Let us now slowly turn the upper crystal, so that the principal
section makes greater and greater angles with that of the first. We
then see four images appear ; each of the two first will be divided,
but the equal intensity which characterized them is not retained in
the others. Of these four images, arranged at the angles of a
lozenge with regular sides, but with unequal angles, two proceed
from double refraction, in the upper crystal, of the ordinary emergent

388 PHYSICAL PHENOMENA. [BOOK m.

ray ; the two others proceed from the double refraction of the extra-
ordinary ray. But an important difference to be indicated is that,
in general, each couple is characterized by a difference in the lumi-
nous intensity of the images. Fig. 261 represents their relative
positions and intensities for angles comprised between 0° and 180° of
the principal sections of the two crystals. If the principal sections
are at right angles, only two images are seen : if they make an angle
of 180° and the crystals have the same thickness, the two images
are superposed ; in the latter case, the deviations made by each
crystal being in opposite directions, there is only one image.

It already follows from this first experiment that each ray of
light which has passed through a doubly refracting crystal, no longer
possesses, after its passnge, the same properties in all directions ; for
in certain directions it is no longer susceptible of undergoing a new

FIG. '262. — Polarization of the ordinary ray l»y double refraction.

bifurcation, and in others, the two rays into which it is divided have
no longer the same luminous intensity. To distinguish these new
properties, it is said that light which has passed through a doubly
refracting crystal is polarized liyht.

But it in important to point out precisely the phenomena just
described. Let us suppose that a ray of solar light, s I (Fig. 262),
is allowed to fall on the first crystal of Iceland spar, its principal
section being vertical. This ray is divided in the plane of the
section into two rays: the one ordinary, IK; the other extra-
ordinary, I E'. If we intercept one of the two by a screen, and
allow the other to pass through a second piece of Iceland spar,
the luminous ray, on traversing the second crystal, will undergo
double refraction : it will be divided into two rays, — i', K, which is
the ordinary ray, and i', R', which is the extraordinary one. Lastly,

CHAP, xvi.] POLARIZATION OF LIGHT. 380

by the help of a lens, we will project the emerging rays on a
screen, and examine what will happen if the second crystal is
turned so as to produce at its principal section every possible
angle with that of the first, from 0° to 360°. Fig, 263 shows the
relative intensities of the two images if the ordinary ray from the
first crystal has traversed the second as in Fig. 262; Fig. 264
shows on the contrary what these intensities are when the extra-
ordinary ray emergent from the first is allowed to pass through the
second prism.

Fin. 263. --Division of the ordinary ray. Variable FIG. 264. — Division </f the extraordinary ray.
intensities of the images of the polarized rays. Intensities of the images of the polarized rays.

We may now sum up. A ray of ordinary light has entered the
first crystal where it undergoes double refraction, and each of the rays
which emerge has particular properties which are distinguished by
saying that it is polarized : for this reason, the first crystal receives
the name of polarizer. The second crystal is used to analyse the
properties which each pencil has acquired by polarization : this is
called the analyser.

The ordinary ray, on passing through the analyser, is divided into
two rays, the intensity of which varies according to the angle the
principal section of the second crystal makes with that of the first,
and which gives two images, one ordinary, the other extraordinary.
If this angle is 0° or 180°, the ordinary image alone exists with
maximum intensity, the extraordinary image having disappeared ;
at 90° or 270° the extraordinary image has attained its maximum
brightness, the other having disappeared. For intermediate positions

390 PHYSICAL PHENOMENA. [BOOK in.

where the second principal section forms angles of 45° with the first,
the two images have the same intensity. Lastly, in other relative
positions of the principal sections of the crystals, there is unequal
intensity in one or other of the images. It is then said that the
ordinary ray is polarized in the plane of the principal section;,
this plane is called the plane of polarization. Now, like the second
ray, the extraordinary ray undergoes the same modifications on pass-
ing through the analyser, with the essential difference that as there
is always a difference of 90° in the relative position of the principal
sections, it is said to be polarized in a plane perpendicular to the
first plane of polarization, Its plane of polarization makes a right
angle with the principal section of the polarizer. Therefore the
two rays, ordinary and extraordinary, proceeding from a ray of light
which has undergone double refraction, are polarized at right angles.

Polarization by double refraction, such as we have just studied in
Iceland spar, is produced in the same manner with all doubly re-
fracting crystals. But it is not always easy to observe it, on account
of the slight separation of the ordinary and extraordinary rays.
With Iceland spar itself it is necessary to have crystals of a certain
thickness, in order that one of the rays may be readily intercepted
with a screen. To obtain this separation of the polarized pencils
some very useful pieces of apparatus have been invented, among
which may be mentioned Nicol's prism.

Nicol's prism consists of a long crystal of Iceland spar which has
been cut in two in a plane perpendicular to the principal section.
The two pieces again placed in their original positions are joined
together by means of a layer of Canada balsam. The refractive
index of this substance is intermediate between the refractive indices
of the spar which correspond, one to the ordinary, the other to the
extraordinary ray. Hence it follows, as has been accurately shown
and confirmed by experiment, that if a ray of light enters in the
direction of the length of the crystal and there divides into two by
double refraction, the ordinary ray undergoes total reflection at the
surface of the Canada balsam, whilst the extraordinary ray alone
passes into the second half of the crystal and emerges from the
opposite face.

Let us suppose that two of Nicol s prisms are used to work out

CHAP, xvi.] POLARIZATION OF LIGHT. 391

Huyghens' experiment. It is evident that only two images will be
obtained, those which proceed from the emergent ray ; that is to say,
from the extraordinary ray polarized by the first prism. If the
principal sections of the two prisms are parallel, one of the images,
the ordinary, is nil, the extraordinary one at its maximum brightness;
if the principal sections are at right angles, both of them disappear,
as the ordinary image which ought to have a maximum intensity
undergoes total reflection, and the intensity of the extraordinary
image is nil. The first prism, that which receives the ray of ordinary
light, is the Nicol polarizer ; the other is the Nicol analyser.

This property of Nicol's prism, of allowing only the extraordinary
ray to emerge, belongs also to a natural crystal, tourmaline, which
when it possesses a certain thickness strongly absorbs the ordinary ray.
M. Biot discovered this remark-
able property in 1815: it will
enable us to quote from Sir J.
Herschel another example of the
polarization of light by double
refraction.

" When we take one of these
crystals and slit it (by the aid of a
lapidary's wheel) into plates paral-
lel to the axis of the prism, of
moderate and uniform thickness
(about ^V of an inch), which must
be well polished, luminous objects
may be seen through them, as FlG" 265-sPe™ of Siberian tourmaline-
through plates of coloured glass. Let one of these plates be interposed
perpendicularly between the eye and a candle, the latter will be seen
with equal distinctness in every position of the axis of the plate with
respect to the horizon (by the axis of the plate is meant any line in
it parallel to the axes of its molecules, or to the axis of the prism
from which it was cut). And if the plate be turned round in its own
plane, no change will be perceived in the image of the candle. Now
holding this first plate in a fixed position (with its axis vertical, for
instance), let a second be interposed between it and the eye, and
turned round slowly in its own plane, and a very remarkable
phenomenon will be seen. The candle will appear and disappear

392 PHYSICAL PHENOMENA. [BOOK in.

alternately at every quarter of a revolution of the plate, passing
through all gradations of brightness, from a maximum down to a total
or almost total disappearance, then increasing again by the same
degrees as it diminished before. If now we attend to the position of
the second plate with respect to the first, we shall find that the maxi-
mum of illumination takes place when the axis of the second plate is
parallel to that of the first, so that the two plates have either the
same positions with respect to each other that they had in the original
crystal, or positions differing by 180°, while the minima, or disappear-
ances of the images, take place exactly 90° from this parallelism, or
when the axes of the two plates are exactly crossed. In tourmalines
of a good colour, the stoppage of the light in this situation is total,
and the combined plate (though composed of elements separately very
transparent and of the same colour) is perfectly opaque."

Thus the beam of ordinary light which has passed through the first
plate of tourmaline is polarized like that which emerges from a crystal
of Iceland spar. All its sides, all its faces, if we may so express it, do
not possess the same property. We shall now see that double refraction
is not the only means of transforming ordinary into polarized light.

In 1808, Malus, a French physicist, famous for his beautiful
researches on optics, while accidentally looking through a crystal of
Iceland spar at -the setting sun reflected by the window-panes of the
Luxembourg Palace, remarked with surprise that, on turning the
prism, the two images changed in intensity ; the most refracted was
alternately brighter or less bright than the other, at each quarter
of a revolution. On minutely analysing this phenomenon, he dis-
covered that reflection at certain angles is sufficient to induce in an
ordinary luminous ray the same properties which a ray possesses after
having traversed a doubly refracting crystal such as Iceland spar.
Huyghens' experiment, concerning which both Huyghens and Newton
had in vain tried to produce a theory, was no longer an isolated phe-
nomenon ; and it was in the endeavour to explain it by Newton's
theory that Malus was led to give the term polarization of light
to the modification undergone by the luminous rays in the ex-
periment just mentioned. Three years later, in 1811, Malus, Biot,
and Brewster discovered, separately, polarization by simple refrac-
tion : Arago, chromatic polarization ; and since then many new facts
belonging to the singular modifications of the luminous rays in the

CHAP, xvi.] POLARIZATION OF LIGHT. 393

phenomena just described have helped to form one of the most
interesting branches of science, as fruitful of theory as of practical
application. As the limits and elementary nature of this work do
not allow us to enter into long details, we can only describe some
of the more remarkable of these phenomena.

And first of polarization ly reflection. When a beam of ordinary
light falls obliquely upon a non-metallic mirror, such as black
glass, marble, or obsidian, it acquires by reflection the same
properties as if it had traversed a double refracting crystal : it is
'polarized.

If a plate of black glass is placed on a table in front of an open
window, and the light of the clouds reflected by the plate obliquely
at an inclination of about 35°, the brightness of the mirror appears
uniform. If, without changing the position, the bright surface is ob-
served through a plate of tourmaline split parallel to its optical axis,
and if this plate is made to turn in its own plane, the following varia-
tions will be seen in the brightness of the image of the clouds formed
on the plate of glass. If the axis of the tourmaline is in a vertical
plane, the image disappears ; the plate of glass seems covered with a
kind of dark cloud : when the axis is, on the contrary, horizontal, that
is to say, parallel to the plate of glass, the darkness completely
vanishes : lastly, in the intermediate positions of the axis of the
tourmaline the brightness of the image gradually increases from the
first to the second position. If the analyser, instead of being a plate
of tourmaline, is a Mcol's prism, the variations of brightness of the
image will succeed each other in the same manner : the minimum will
take place when the principal section of the prism is vertical, and the
maximum when this section is at right angles to its first position.

From these experiments we infer that a luminous beam falling
with an inclination of 35° 25' (or, in other words, with an incidence
of 54° 35') on a plate of black glass, is, after reflection, polarized in
the plane of this reflection. This angle of 54° 35' is what is named
the angle of polarization of glass : it is that in which the reflected
ray can be completely extinguished by the polariscope analyser.
This is expressed by saying that it is completely polarized. When
the angle of incidence has another value, the image of the beam
is not completely extinguished ; in fact, the reflected ray is only
partially polarized.

H H

394

PHYSICAL PHENOMENA.

[BOOK in.

The angle of polarization varies with the nature of the reflecting
substances. Thus, it is 52° 45' for water, 56° 3' for obsidian, 58° 40'
for topaz, 68° 2' for diamond. Brewster made a very curious experi-
ment in order to prove the difference which we shall presently point
out between the angles of polarization of two substances, — glass
and water £or example.

He placed a plate of glass so that it might receive and reflect a
beam of light at an incidence of 54° 35', which is, as we have just
seen, the angle of polarization of glass. He then observed the
reflected beam with an analyser, in such a manner that all light
disappeared. Now, if at this moment any one breathed on the

Fio. 266. — The polariscope of Malus perfected by M. Biot.

glass plate, the image again appeared. This phenomenon is due
to the reflection from a bed of water, the angle of polarization of
water not being the same as that of glass.

CHAP. XVI.]

POLARIZATION OF LIGHT.

395

Malus invented an apparatus by the aid of which all the pro-
perties of polarized light by reflection can be studied. Besides those
we have just described, there are others which characterize this light
when it is reflected after falling on a second reflecting plate. Fig.
266 represents the apparatus of Malus modified and perfected by M.
Biot. I is the polished plate for polarizing the ray of light s I by
reflection from the surface of the plate ; the reflected and polarized
ray 1 1, then enters a tube blackened inside and furnished with dia-
phragms, and passes along its axis.

As it issues from the tube, the ray falls on a plate i' of black glass,
is again reflected, and either falls on the eye, or forms an image on a
screen E. The frames which hold the two reflecting plates can be
turned round on an axis perpendicular to that of the tube, so that
their planes can make with the latter all possible angles ; moreover,
each plate can be turned
in one of its positions
also round the axis of
the tube; so that for a
given incidence of the
luminous ray on the first
plate, both the angle of
incidence of the polar-
ized ray on the other
plate, and the angle of
the second plane of re-
flection with the first, can
be varied at will. By
means of this apparatus
it can be shown that the
maximum brightness of the image takes place when the two planes
of reflection coincide ; and the minimum when these two planes are
at a right angle, Moreover, the ray is completely extinguished when
the angle of incidence on each of the two mirrors is 35° 25', provided
always that the beam has not, as in the case of solar light, too great
an intensity. Bvewster discovered a very simple law which exists
between the angle of polarization and the index of refraction of the
substance which polarizes light by reflection, so that, if one of these
elements is .known, we can deduce the other. This law expresses

H H 2

FIG. 267. — Relation between the polarized ray and the
angle of polarization of a substance and the re-
fracted ray. R' i r is the right angle.

396 PHYSICAL PHENOMENA. [BOOK in.

the following geometric relation : the reflected ray I R, polarized at
the angle of polarization, and the refracted ray ir, form a right
angle. Simple refraction also polarizes light. This was discovered
separately by Mains, Biot, and Brewster in 1811. The phenomenon
can be proved by Biot's apparatus (Fig. 266) when the glass I has
been replaced by a glass prism. If the prism is turned so that the
ray issues perpendicularly to the face of emergence, it is found,
by turning the analyser i', that .the beam after reflection shows a
maximum and minimum intensity, but not in a very decided manner.
The light then is partially polarized : as the maximum of brightness
takes place when the plane of incidence on the analyser is perpendi-
cular to the place of incidence on the prism, we see that in this case the
plane of polarization is perpendicular to the plane of refraction.

A completely polarized ray can be obtained by simple refraction
if we cause it successively to traverse several parallel plates of glass
at an angle of 35° 25', which is, as we have seen, the angle of polar-
ization of glass. These thin and polished plates must be laid one
on the other, in such a way that a thin stratum of air is inter-
posed between each plate : the apparatus thus arranged is called a
glass pile ; it is used as a polariscope by placing it in Biot's appa-
ratus in place of the glass i'. We will not enlarge further on
this curious class of phenomena, the detailed description of which
would detain us too long, and which, besides, to be well understood,
would require difficult theoretical developments. We only desire
to initiate the reader into the fundamental facts the discovery of
which has been the starting-point of this important branch of
modern optics.

CHAP, xvii.] CHROMATIC POLARIZATION. 397

CHAPTER XVII.

CHROMATIC POLARIZATION.

" TTTHILE examining in a clear light a somewhat thin plate of mica
VV by means of a prism of Iceland spar, I observed that the two
images did not possess the same tint of colour; for one was greenish
yellow, while the other was reddish purple, and the portion where
the colours overlapped presented the ordinary colour of mica as seen
by the naked eye. I noticed at the same time that a slight change
in the inclination of the plate as regards the rays which traversed it
caused a variation in the colour of the two images ; and that if this in-
clination were allowed to remain constant and the prism in the same
position, the plate of mica was caused to turn in its own plane. I found
four positions at a right angle in which the two prismatic images were
equally bright and perfectly white. If the plate of mica were left afc
rest while the prism was turned, each image was observed successively
to acquire different colours, and to become white after each quarter
of a revolution. In addition to which, for all positions of the prism
and the plate, whatever might be the colour of one of the images, the
other always presented the complementary tint ; and wherever the two
images were not separated by the double refraction of the crystal, the
mixture of the two colours formed white."

It was in these terms that Arago, in a memoir read at the Academic
des Sciences on the llth of August, 1811, described the experiment
which was the beginning of a series of discoveries on the phenomena

398 PHYSICAL PHENOMENA. [BOOK in.

of coloration of polarised light. He instantly recognised that the light
transmitted by a plate of mica was light polarized by reflection from the
atmospheric strata : in dull weather, when the light from the clouds has
the nature of common light, the two images seen through the plate of
mica would show no trace of colour. Thus, in order to produce the
phenomenon, the light which traverses the crystallized plate must have
been previously polarized. This condition was placed beyond doubt by
Arago, by means of several experiments in which he received, on a
plate of mica, rays reflected by a mirror of black glass : he then noticed
that the colours of the two images observed through Iceland spar
were brighter when the light was reflected at an angle nearer to the
angle of polarization of the glass. All doubly refracting substances
cut in thin plates parallel to the axis, possess this same property of
colouring the polarized light which traverses them ; thus plates of
gypsum (sulphate of lime) can be used, also rock-crystal and Iceland
spar. But the thicknesses of the plates which produce these colours
vary in different substances, and in the case of each of them no
coloured images can be obtained if the thickness is not comprised
between certain limits. A plate of sulphate of lime must have more
than 0 mm. 425, and less than 1 mm. 27, of thickness ; a plate of mica
less than 0 mm. 085 ; a plate of rock-crystal less than 0 mm. 45. It is
difficult to obtain colours with Iceland spar, because the thickness* of
the plate must not exceed the fortieth part of a millimetre. The in-
clination of the plate to the direction of the polarized rays influences
the colours, which quickly change as this inclination varies. The
thickness with the same inclination of the plate and the same posi-
tion of the prism also influences the colours of the image ; and M. Biot
found that the laws of variation of these shades or tints are precisely
those which Newton discovered for the coloured rings of thin plates
obtained by the superposition of two lenses; but the thicknesses
of the doubly refractive plates which correspond to the colours of
Newton's various orders are much greater than those of the stratum
of air inclosed between the lenses.

This property of the change of colour, according to the thickness,
is employed to produce varied and curious effects. If, after having
fastened a plate of gypsum on a piece of glass, a spherical cavity of
large radius is hollowed out, and the plate is examined by means
of Biot's apparatus, the light which reaches the eye, having been

CHAP. XVII.]

CHROMATIC POLARIZATION.

399

previously polarized before traversing the plate of gypsum and the
analyser, a series of coloured concentric rays are seen, like those
observed round the point of contact of the two lenses ; if we engrave
different objects in the hollow of the plate, — such as flowers, insects,
and butterflies, — the depths of the engraving can be calculated
at the different points, so as to reproduce the bright and varied
colours of the natural objects. " Formerly
we did better," said Mr. Bertin, recently, in
a very interesting conference on polarization,
" and profited by the circumstance to do
honour to the author of these beautiful ex-
periments. In the midst of a crown of leaves
appeared the name of Arago, with the date
of his discovery. From the contemporaries
of the great man it was perhaps flattery ; but
now that he is no more, the suppression of
this experiment in a course of physics is
an act of ingratitude : we forget our dead to
run after butterflies." It would be just to
join to the name of Arago that of Brewster,
who at the same time made nearly the same
discoveries, and to whom we principally owe
that of coloured rings in crystals with one or
two axes. Before entering into details of
these remarkable phenomena, we may state
that glass, in the ordinary state, is not sus-
ceptible of showing the colours observed in
crystallized plates, but it acquires this pro-
perty by tempering, bending, and compres-
sion, and by the action of heat. Figures
268 and 269 show some of the appearances presented under these
different circumstances by plates of glass of a certain thickness,
and of either a rectangular or square form. The discovery of
these phenomena is due to Seebeck (1813), and they are of the
same nature as those just described. The following is a curious
experiment of Biot related by M. Daguin in his "Traite de Phy-
sique : " — " Biot produced longitudinal vibrations in a band of
glass about two metres in length, placed between the polarizer and

FIG. 268 — Colours of polarized
light in compressed glass.

400

PHYSICAL PHENOMENA.

[BOOK in.

the analyser of his apparatus (disposed so as to show darkness) ; at
each vibration he saw a bright line shine out, the brightness and
colour of which depended on the mode of friction, and on its
intensity."

The colours of polarized light, produced by the passage of a beam of
this light through a thin crystalline plate, depend, as we have already
seen, on the thickness of the plate ; it varies, if the thickness itself
varies. But for a certain thickness, the tint is uniform, because all
the rays which compose the beam are parallel, and thence traverse
the same space in the interior of the plate. If instead of a beam a
conical pencil of polarized light is received on the plate, so that the

Fio 269. —Colours of polarized light in unannealed glass.

axis of the cone is perpendicular to the surface of the plate, it is clear
that the rays will pass through the interior of the crystal in paths
which will be longer as their distance from the axis increases, and the
tint of the plate, observed by means of an analyser, will no longer be
uniform. We then see systems of coloured rings, the forms and tints of
which vary according as we are dealing with a crystal with one or two
optical axes, and according to the position of the polariscope in regard
to the plane of polarization. The following is the manner in which
these beautiful phenomena are obtained. A tourmaline pincette or
forceps is used (Fig. 270). This instrument consists of two metallic
rings with a spring in the form of tweezers, which presses them

CHAP. XVII.]

CHROMATIC POLARIZATION.

401

together, and in each of which a plate of tourmaline is encased ;
each plate is capable of turning in its ring, so that, at will, it may
be placed in all possible angular positions in regard to the axes
of the two crystals. Between the two rings is interposed, for
instance, the thin crystallized plate of Iceland spar fixed to a
cork disc, which the pressure of the rings holds between the tour-
malines. If we look through this system of three plates, we at
once perceive the coloured rings. The plate of tourmaline turned
towards the sky polarizes the light of the clouds, which, after having
traversed this first plate, converges towards the eye in passing through
the plate of spar and the second tourmaline. Let us suppose first
that the two tourmalines are disposed in such a
manner that their axes are perpendicular : the
primitive plane of polarization is then parallel to
the principal section of the tourmaline which
serves as a polariscope. A series of concentric
iridescent rings is seen traversed by a black
cross. If the polariscope is then turned 90°,
the axes of the tourmalines will be parallel,
and the principal section of the polariscope will
be at right angles to the plane of polarization.
The black cross is then found to be replaced
by a white one, and the iridescent rings show}
at the same distance from the centre, colours
complementary to those which they assumed
in the first experiment. In the intermediate
positions of the axes of the tourmalines, the first
appearance gradually passes into the second.

These phenomena are presented in the case of white light. If
homogeneous light is used, yellow light for instance, rings are ob-
tained alternately bright and black, having crosses similar to those
seen in the preceding experiment, the bright rings being of a yellow
colour. Eings of the same kind would appear whichever of the
colours of the spectrum were employed, and would be larger the
higher the refrangibility of the colour : for this reason the rings are
iridescent when white light is employed, and this is why the violet
occupies, in this case, the outer edge of each ring in the first position
of the polariscope.

I I

FIG. 270.— Pincette of
tourmaline.

402 PHYSICAL PHENOMENA. [BOOK in.

In 1813 Brewster discovered the coloured rings produced by polar-
ized light when it traverses thin plates of doubly refracting crystals :
he saw them first in the ruby, emerald, topaz, in ice, and nitre ; later,
Dr. Wollaston observed them in Iceland spar. By studying these
phenomena in the different crystallized substances Brewster succeeded
in dividing doubly refracting crystals into two classes, viz. crystals
with one axis and crystals with two axes ; and this he effected by the
following means : — Whilst, in the ruby, emerald, and Iceland spar, for
example, he only observed a simple system of coloured rings, in nitre
and topaz cut in a certain direction and observed through the tour-
maline pincettes he observed a double system of rings, alternately
black and bright, if the polarized light which traverses them is
homogeneous, and iridescent if this light is white. This pheno-
menon led Brewster to the discovery of crystals with two axes.

To observe the rings of which we speak, a plate of nitre is cut
perpendicularly to the mean line of the two axes, and is placed
between the rings of the tourmaline pincettes.

With homogeneous light, rings are obtained alternately which are
black and bright, the latter being of the colour of the light-source.

If the plate remains fixed between the two tourmalines and the
analyser is turned (that is to say, the tourmaline near the eye), the
rings without changing their position gradually change in colour, and
when the rotation is 90° or 270° these colours become complementary
to those which the rings first assumed in the same position of the
plate : the black crosses have been replaced by white ones.

We must pause here in our description of the phenomena produced
by polarized light; they are most interesting, and the very enu-
meration of them would require many pages. The reader however
will be glad to know that, for the expenditure of a few shillings
and of some time, he may produce most of these beautiful pheno-
mena for himself. Wre have proposed to ourselves rather to excite
his curiosity, and to induce him to undertake a more complete study
of natural philosophy, than to give him a precise notion of the
causes of these phenomena ; that is to say, to show what explanation
they receive according to the undulatory theory. We cannot help
however giving a resumt in a few lines of the important progress
which that theory has made, under the influence of the discoveries
which succeeded each other so rapidly at the beginning of our century.

CHAP, xvii.] CHROMATIC POLARIZATION. 403

In a preceding chapter we have noticed that luminous pheno-
mena are due to the vibratory movement of the elastic medium called
the ether. Phenomena of interference, inexplicable by the theory of
emission, find the most simple and satisfactory explanation on the
undulatory theory ; but they tell us nothing as regards the direc-
tion in which the vibrations of ether take place. We can sup-
pose with equal plausibility that the oscillations of a molecule are
affected either in the direction of the propagation of light, or in a
direction parallel to the surface of the waves, or perpendicular to the
luminous ray, or lastly, in any direction oblique to this ray.

But adopting the first hypothesis, — that which assimilates, so to
speak, the luminous waves to sonorous waves, — it would be impossible
to understand the transformation that a luminous ray undergoes, when
it has traversed a doubly refracting medium, or when it is reflected at
a certain angle from the surface of a polished body. Why, if the
vibrations are longitudinal, should the polarized ray possess particular
properties in certain planes ? Why should these properties belong
exclusively to certain sides of the ray ? These objections had given a
great blow to the undulatory theory, till Fresnel conceived the idea of
substituting for the hypothesis of longitudinal vibrations, that of
transversal vibrations perpendicular to the direction of the luminous
propagation. A ray of ordinary light therefore becomes one in which
tfee vibratory movements are effected successively in all directions on
the surface of the wave that is perpendicular to the line of propaga-
tion ; hence its properties must be the same in all directions. But if
this ray passes through a polarizer, on emerging, the vibrations of
which it is composed, instead of being effected in all directions,
become parallel, and are all effected in one plane passing through the
ray. The polarizer has, so to speak, sifted the vibrations of the
ray of common light: it has stopped or destroyed some, and has
allowed those vibrations only to pass which are in the plane of the
principal section. More accurately, every vibration parallel to the
principal section passes without alteration through the crystal, while
every perpendicular vibration is destroyed : and all vibrations oblique
to the two first are decomposed into others, — one parallel to the prin-
cipal section of the polarizer, which passes ; the other perpendicular,
which is stopped. From this cause arise the properties of polarized
light which we have described.

I I 2

404 PHYSICAL PHENOMENA. [BOOK in.

The consequences of the undulatory theory thus modified are very
numerous : until now they have all been proved by experiment; or
rather, the phenomena found by observation are explained, like those
deduced from theory, with an exactitude which is the most striking
proof of the truth of the principles which constitute the undulatory
theory.

Let us add a few lines on the applications of polarized light in the
study of the natural and physical sciences.

Arago used polarization by double refraction to construct a pho-
tometric apparatus based on the relative intensity of two images :
an intensity, the law of which was enunciated by Malus. The same
philosopher has indicated a means of distinguishing rocks under the
sea which are hidden by the brightness of the light reflected from
the surface. Looking through a Nicol's prism, the principal section
having been carefully placed vertically, the reflected rays are ex-
tinguished ; and the refracted rays being alone transmitted to the eye,
reveal the presence of the submerged rocks.

Polarization enables us to know whether the light which comes to
us from a substance has been reflected from its surface. It is in this
way that we may determine the nature of the light of the heavenly
bodies, which, like the moon and planets, simply send us the sun's
rays ; and it has been stated that the light of cometary masses is
partly borrowed from the sun, many observers having distinguished
traces of polarization in a plane passing through the sun and the
nucleus. The polariscope also is a valuable ally in eclipse observa-
tions. The light of the rainbow is polarized in a plane normal to the
bow and passing through the eye of the observer. We shall learn
indeed that the rainbow is formed of light reflected by the spherical
drops of rain. Arago made use of polarization by reflection to
discover the nature of various precious stones : having cut a small
facet on the surface of one of them, he determined the angle of
polarization, and noticed that it was exactly that of the diamond.
Chromatic polarization is of great help in the study of crystals : it
indicates whether a crystal has one or two axes of symmetry, as also
the position of these axes in the crystal, &c.

Lastly, quartz and a great many liquids, solutions of sugar, solutions
of tartaric acid and albumen, all have a property characterized by
physicists as the rotatory power : a plate of quartz cut perpendicularly

CHAP, xvii.] CHROMATIC POLARIZATION. 405

to the axis causes the plane of polarization of the rays which traverse
it to deviate through a certain angle ; and this deviation is different for
rays of different colours. If the polarized light which has traversed
the quartz is white, the colours which compose it will be destroyed
in different proportions : hence a certain tint proceeding from the
mixture of the rays which are not extinguished. This is the pheno-
menon of rotatory polarization discovered hy Arago in 1811, and the
laws of which Biot has studied experimentally.

Now these laws have furnished a valuable method in the arts
called saccharimetry, by the aid of which the quantity of pure sugar
contained in a solution of sugar can be discovered.

These phenomena therefore, which seemed at first only interesting
in theory, can be brought to bear on important practical processes.

406 PHYSICAL PHENOMENA. [BOOK HI.

CHAPTER XVIII.

THE EYE AND VISION.

Description of the human eye — Formation of images on the retina — Distinct vision
of the normal eye — Conformation of the eyes in Myopsis and Presbyopsis.

numerous and varied phenomena which we have just
J- described all relate to the propagation of light through different
media, and to the modification it undergoes, either in point of intensity
or colour, when the conditions of the path followed by the luminous
rays are changed. We have not occupied ourselves yet with the
manner in which our organs are affected by all these phenomena, nor
with the path followed by the light when it ceases to belong to the
outer world and becomes an internal phenomenon.

How is this passage effected ? by what transformation does a
vibratory movement, such as that of ether waves, succeed in pro-
ducing in man and other animals the sensation of sight ? How do
variations in the velocity or in the amplitude of the vibration produce
corresponding variations in the intensity of light and colours of bodies?

•This is a series of questions which science is far from having
solved, and which moreover belong rather to the domain of physiology
than to physics.

That which is known and which observation has investigated in a
positive manner is the path of the luminous rays in the eye, from
the instant when they penetrate that organ to the moment when
they reach the nerves ; the impression they then produce is trans-
mitted to the brain and determines the sensation of sight. During
this passage, the luminous rays obey, as we shall see, the known laws
of propagation of light through media of variable form and density ;
we are dealing only with phenomena of simple refraction.

The eye is nothing more than a dark chamber, the opening of which
is furnished in front with a transparent window, behind which there is

CHAP, xviii.] THE EYE AND VISION. 407

a lens ; and the back of which is covered with a membrane, which
serves as a screen upon which the images of exterior objects are pro-
jected and reversed. We shall now give a detailed description of this
admirable instrument.

The eye is placed in a cavity of the skull known as the orlit ; its
form is that of a nearly spherical globe entirely covered by a hard
consistent membrane, the resemblance of which to horn has caused
it to be called the cornea where it is transparent in front, and else-
where the sclerotic.

Fia. 271.— Horizontal section of the eyeball. Scl. the sclerotic coat ; Cn. the cornea ; E. the
attachments of the tendons of the recti muscles ; Ch. the choroid ; C.p. the ciliary processes ;
C.m. the ciliary muscle; Ir. the iris; Aq. tire aqueous humour ; Cry. the crystalline lens;
Vi. the vitreous humour ; Rt. the ictina ; Op. the optic nerve; M.I. the yellow spot. The
section has passed through a ciliary process on the left side, and between two ciliary pro-
cesses on the right.

The cornea, in front of the eye, has a much more marked curvature
than the sclerotic ; it is like a very convex watch-glass.

Through the transparent cornea is seen a circular membrane, the
colour of which varies according to persons and races ; sometimes grey,
light or dark blue, or sometimes a yellow brown. This membrane is
the iris, a kind of diaphragm pierced in the centre by an aperture
which is circular in man ; this opening is called ihepupil. Behind the
pupil which is the opening of the dark chamber there is a solid lens ;
this is the crystalline lens, the outer face of which presents a less
decided curve than the inner. The crystalline lens divides the cavity of

408 PHYSICAL PHENOMENA. [BOOK m.

the eye into two parts or chambers of unequal dimensions, as shown
in Fig. 271. The anterior chamber, placed between the transparent
cornea and the crystalline lens, is full of liquid, differing very little
from pure water, and with nearly the same refractive power ; this
liquid is called the aqueous humour. Between the crystalline lens and
the back of the eye is the posterior chamber, which is filled with a
transparent colourless substance having the consistence of a jelly,
and rather more refractive than water : it is the vitreous humour.

A ray of light which penetrates into the eye traverses the following
series of refractive media, before arriving at the back of the organ : the
transparent cornea, the aqueous humour, the crystalline lens, and the
vitreous humour. In each of these media the light undergoes a par-
ticular refraction, and the whole deviation is such that it comes to a
focus on the membrane which covers the posterior chamber of the
eye. All the inner surface of the sclerotic is covered with a thin
membrane, the chor-oid.

The choroid coat is lined internally with a layer of polygonal
bodies containing pigments ; these are called pigment cells. Inside
these lies the retina, sections of which are given in the next figure.

Those parts of the eye that we have just described tend to the
formation and reception of the images of objects ; their functions are
therefore passive. It is on the retina where these images are produced
that the impression of light on the sensible part of the eye takes
place. Behind the globe of the eye, the choroid and the sclerotic are
pierced with a circular hole, which gives passage to the filaments of
the optic nerves. This fasciculus, or sheaf, on arriving at the interior
of the eye, is spread out and extended over the whole surface of
the sclerotic, forming a membrane immediately in contact with the
vitreous humour.

Here, then, we have a lens to throw an image; the eye is a
" water camera," and the retina is the equivalent of the photographer's
ground glass or prepared plate, where the vibrations of the ether are,
in Professor Huxley's language, converted into a stimulus to the
fibres of the optic nerve, which fibres when excited have the power
of awakening the sensation of light in us by means of the brain. But
it must not be forgotten that the fibres of the optic nerve are as blind
as any part of the body ; " but just as the delicate filaments of the
ampullae, or the oloconia of the vestibular sac, or the Cortian fibres of

CHAP. XVIII.]

THE EYE AND VISION.

409

the cochlea, are contrivances for converting the delicate vibrations of
the perilymph and endolymph into impulses which can excite the
auditory nerves, so the structures in the retina appear to be adapted
to convert the infinitely more delicate pulses of the luminiferous
ether into stimuli of the fibres of the optic nerve."

FIG. 271 A.— Diagrammatic views of the nervous (A) and the connective (B) elements of the
retina, supposed to be separated from one another. A, the nervous structures — b, the rods ;
c, the cones ; &' d, the granules of the outer layer, with which these are connected ; d d', inter-
woven very delicate nervous fibres, from which fine nervous filaments, bearing the inner
granules, //', proceed towards the front surface ; g g', the continuation of these fine nerves,
which become convolrated and interwoven with the processes of the ganglionic corpuscles, h h' ;
i i, the expansion of the fibres of the optic nerve. B, the connective tissue— a a, external or
posterior limiting membrane ; e' e', nuclei ; d d, the intergranular layer ; g g the molecular
layer ; I, the anterior limiting membrane. (Magnified about 250 diameters.)

It is easy to account for the path of the rays of light which
emanate from an object A B, and the manner in which this object
forms its image on the retina. This lenticular system, composed of
the transparent cornea and the crystalline lens separated by the
aqueous humour, has its optic centre at the point o situated a little
behind the crystalline lens (Fig. 272).

If the secondary axes, A o and B o, are taken, it is in their prolonga-
tion and at the point where they meet the retina that the beam ema-

410 PHYSICAL PHENOMENA. [BOOK in.

nating from the points A and B converges ; the intermediate points will
form their images between the positions a and 6. The images b a of
the object will then be reversed. This result is one of the conse-
quences of the laws of refraction and of the path of rays through
lenses ; but it has been proved by direct observation. Thus, by taking

the eye of an animal just dead and
freeing it from the strata of fat
with which the ball is enveloped,
the sclerotic is pared off at its
posterior part, in such a manner a's
to render^ it translucent : the eye
thus prepared, and exposed to day-
light, shows on the sclerotic a very

objects. The reversed image of a

candle can also be seen through the sclerotic of albino animals ; the
absence of colouring pigment in this sclerotic renders it naturally
translucent.

The iris acts as a diaphragm, which only allows cones of light,
having the aperture of the pupil for their base, to penetrate into
the eye.

But the iris can be spontaneously contracted or dilated, in such a
manner as to cause the pupil to become narrower -or larger. This
automatic movement is produced in the first direction when the
brightness of the light received by the eye increases ; and in the
second direction if this brightness diminishes. The same thing occurs
when the eye looks at objects situated at different distances ; the
pupil enlarges for distant objects and contracts for objects nearer
the eye.

Look at the eye in a looking-glass when you hold it at a certain
distance, and examine the dimensions of your pupils ; then rapidly
draw the mirror nearer without moving the pupil : you will see the
iris slowly get narrower.

The eye being thus assimilated to a system of lenses, it may
appear singular that it can be used to see clearly so many objects
situated at such varied distances. It cannot be doubted that in
order that the vision be distinct, the object must make its clear
image on the retina itself.

CHAP. XVIII.]

THE EYE AND VISION,

411

It is necessary then, when the distance changes, that the focus
should change also, so as always to coincide with the surface of the
nervous membrane. This fact is explained by saying that the eye ac-
commodates itself to distances. But by what mechanism does the eye
in this way keep its property of clearly distinguishing objects ? For
short distances, the narrowing of the pupil ; and for long ones, a change
in the form of the crystalline lens which diminishes its converging
power: such are the two movements submitted to our will, but made
without our knowledge, by the aid of which physicists explain the
adaptation of which it is capable. There is an inferior limit to the
distance of objects that we try to see clearly : this is the limit of
distinct vision, which varies with individuals and with age, between
six to eight inches. In a nor-
mally constituted eye, there is no
superior limit.

The conformation of the eye may
be such, that the limit of distinct
vision may be much greater than
that of which we have just spoken.
This affection, which is met with
especially in old people, obliges
them to hold a book at a great

distance to read it clearly. That is because the image is formed
beyond the retina, so that the convergence of the rays emanating
from a luminous point does not
fall on this membrane, whence a
confused impression results. By
taking the object to a distance, the
focus is brought forward, and vision
becomes more distinct. Persons
with this defect of sight are long-
sighted : this is attributed either to
the diminution of the crystalline
lens or to a rigidity which does not

permit of adaptation to small distances, or lastly to a flattening of the
globe of the eye ; near-sighted people have the opposite defect. The
distance of distinct vision is much shorter for them than for normal
sight, and at great distances the sight is always confused. This arises

FIG. 273.— Formation of the image in the
eye of a long-sighted person.

FIG. 274. — Formation of the image in the
eye of a short-sighted person.

412 PHYSICAL PHENOMENA. [BOOK in.

from an opposite cause to that which produces long-sight : the focus or
the image of a luminous point is formed in front of the retina. The
extreme convexity of the crystalline lens and the large diameter of
the globe of the eye are the most ordinary causes of short-sightedness
This defect is acquired by habit : literary and office men, and people
whose occupations oblige them to look closely at small things, are
frequently subject to this infirmity.

Many physicists have inquired why the images of objects, being
reversed on the retina, are seen in their real positions ; that is to say,
•upright. To explain this apparent singularity, hypotheses more or
less ingenious have been suggested. But the image projected on the
retina is not an object that we might examine, as if we possessed
another eye behind the retina. In truth, outer objects and ourselves,
our own bodies, are seen by us in their exact relative positions : this
is all that is necessary, and when we say that we see an object, a tree
for example, upright and not inverted, that simply means that its top
and its base appear to us, the first to be raised in the air, the other
touching the ground, absolutely in the same direction as our own head
and feet in our normal position. If, by a particular disposition of one
eye, similar to that of certain lenses, the images were made upright on
the retina, it does not appear doubtful to us that our perception would
not be changed : in order to make it otherwise, it would be necessary
that there should be an exception for the image of our body, which is
beyond supposition.

The impression made by light on the retina ]asts a certain time,
which accounts for our seeing under the form of a luminous line
a bright point which moves rapidly : thus the end of a stick, being
lighted, by rapid turning takes the form of a circle of fire. Some
experiments made by M. Plateau prove that the mean length of
sensation is eight- tenths of a second ; that the light must persist a
certain time in order that the impression produced arrive at its
maximum, and that the length of this maximum time is in the
inverse -ratio of the brightness ; lastly, that the duration of the total
sensation increases with the intensity of the light.

BOOK IV.

HEAT.

BOOK IV.
HEAT.

CHAPTEE I.

DILATATION. — THERMOMETERS .

Sensations of heat and cold ; causes of error in the'perception of the temperature
of bodies — General phenomena of dilatation and contraction in solids, liquids,
and gases — Temperature of bodies — 'Thermometers based on dilatation and
contraction — The mercurial thermometer — Alcohol thermometer — Air ther-
mometers ; metallic thermometers.

ALL known substances, whether solid, liquid, or gaseous, appear to
the touch more or less warm or cold. This impression, as daily
experience shows, depends as much on the particular disposition of
our organs as on the condition of the bodies themselves ; moreover
it may chance that they do not produce in us any sensation of heat ;
in a word, they may appear neither hot nor cold.

The same body, when we touch it at different times, may also
produce in us different and even opposite sensations, either because
it is really in the interval warmed or cooled, or because our organs
have undergone analogous modifications ; or, lastly, the two causes to
which we have here referred may have simultaneously contributed to
the differences of impression. Anyone can easily find examples of
the influence of these two causes, and we can understand how difficult
it would be to appreciate variations in the temperature of bodies, if the
basis of this appreciation were only the personal sensations produced
by contact, or at a distance. Let us suppose, for example, that we hold
our light hand for some time in a vessel of cold water, and our left in

416 PHYSICAL PHENOMENA. [BOOK iv.

one of very warm water, and that we afterwards plunge them both at
the same time into a third vessel filled with lukewarm water ; we
shall undergo simultaneously two opposite sensations, one of heat, the
other of cold, both proceeding, nevertheless, from the same body in the
same condition.

Another example of the difficulty which we have pointed out exists
in the fact that the outer air appears to us cold if we leave a warm
room ; and, on the contrary, the same air seems warm when we come
out of a cool cave. On entering a well-warmed room in frosty weather
we declare that the temperature is unbearable ; nevertheless, in warm
weather, if the air suddenly cools, we shall shiver in the same tempe-
rature which would appear excessively high in winter. This is because
our organs, which are gradually habituated to the cold or heat, with
difficulty undergo the quick transitions which determine in them more
intense sensations. It is not therefore possible to make use of such
variable impressions in the determination, however inexact, of the
thermic condition of bodies.

Hence the necessity of finding among the effects which result from
the variations of temperature in solids, liquids, and gases, a phenomenon
sufficiently general and constant to be used as a point of comparison
in studies of this nature ; that is to say, a phenomenon, the variations
of which can be verified and measured, without the necessity of the in-
tervention of the personal impressions of the observer. Now, physicists
have ascertained the fact — general with one or two exceptions, some
apparent, others real — that all bodies, whatever their physical state, on
being heated, increase in volume or dilate, and on being cooled contract
or diminish in volume. We shall first describe some experiments
which demonstrate this phenomenon, in solids, liquids, and gases.

If we take a metal sphere and ring of the same substance, of such
dimensions that when they are at the same temperature the sphere
can just pass through the ring, and if the ball alone be now heated and
placed on the ring, it will no longer pass through, which proves that it
has been expanded by heat ; but if it is allowed to cool and return to
its original condition, it again passes through. If, on the other hand,
the ring is warmed, the metal sphere passes freely through the open-
ing, whence it may be concluded that the ring has been enlarged
by the heat. But, if the ring and the sphere are heated at the
same time, and equally, both increase in volume to a like extent,

CHAP. I.]

DILATATION.

417

and they preserve the same relationship as regards size as at the com-
mencement. This little apparatus is known as S'Gravesande's ring,
from the Dutch physicist who invented it. Sometimes it takes another

FIG. 275. — S'Gravesande's ring. Expansion of solids by heat.

form (Fig. 276) ; for the sphere a metallic cone is substituted, on which
the ring slides to different heights according as the ring or the cone is
alone heated. If the increase of temperature is the same for the cone
and the ring, that is to say, if both are uniformly heated, although
separately, the ring descends on the cone to an in-
variable position. This last fact furnishes us with an
important indication as to the manner in which vases
which are cylindrical, conical, or of other forms, are
dilated. Their change of volume takes place as if the
vase were filled with the substance which forms the
envelope : its interior capacity varies, as the volume of
the solid nucleus of which we speak itself varies, under
the same thermic conditions.

Bodies expand by heat equally in every direction, so that a metallic
rod having the form of a parallelepiped increases in each of its three
dimensions, width, length, and thickness. Hence there are three kinds
of expansion — cubical, superficial, and linear expansion. The last
is proved by means of the apparatus represented in Fig. 277. A
metallic rod is fixed at one of its extremities, and when heated along
the whole of its length it dilates freely at the other extremity, which
presses against the little arm of a bent lever so that the index form-
ing the large arm of the lever describes, on a graduated scale, an arc

K K

FIG. 276.— Ex-
pansion of
solids.

418 PHYSICAL PHENOMENA. [BOOK iv.

which is larger as the proportion between the lengths of the two
branches increases. The smallest amount of expansion of the rod
is thus rendered perceptible.

FIG. 277.— Linear expansion of H solid rod-

Variation of temperature produces much more decided variations
of volume in liquids than in the greater number of solids. The
following is one of the means which is used to demonstrate the
expansion of liquids.

We take a glass bulb, to which is attached an open tube of small
diameter ; we fill it with the liquid to be experimented upon, and mark
upon it a line a to indicate the position of the liquid in the tube
(Fig. 278). Then, plunging the bulb into water warmer than the liquid,
the movement of the latter can be easily followed in the tube. At first
the level is seen to descend from a to & ; which arises from the expan-
sion of the glass envelope, which responds to the first action of the
heat. Hence its capacity is increased, before the liquid within can
compensate for this augmentation by its own expansion. But after
a short time the apparent contraction ceases, and the liquid gradually
rises to, say, the point a', where it remains if equilibrium has been
established. If the apparatus is now cooled, the liquid wil^be seen
to descend gradually, until at last it assumes its original height.

Different liquids do not expand equally under the same conditions,
but, with about one exception, to which we shall soon advert, they all
increase or diminish in volume, according as they are heated or cooled.

Again, gases are still more expansible than liquids : if we place

CHAP. I.]

DILATATION.

419

near the fire a closed bladder half filled with air, we observe that it
gradually swells out ; the air which it contains therefore increases in
volume by the action of heat. The expansion of air, or any other gas,
under the influence of an increase of temperature, may be proved by
other means. If we take a glass bulb provided with a long capillary
tube open at its extremity (Fig. 279) and filled with the gas the

Fio. 278.— Expansion of liquids by heat.

FIG. 279.— Expansion of gases by heat.

expansion of which we desire to illustrate, and which is separated
from the outer air by an index of mercury; immediately that the
bulb is slightly warmed, by the contact of the hands for example,
the interior gas also becomes warm, expands, and drives the index
from the reservoir. When the gas has cooled, its volume diminishes,
and the index again assumes its original position. By using a doubly

K K 2

420

PHYSICAL PHENOMENA.

[BOOK iv.

bent tube (Fig- 280) containing some liquid at the lower curve, the
expansion is seen by the rising from a to b of the liquid in the arm
most distant from the bulb, whilst the level descends in the other.

Let us confine ourselves for the present to the phenomenon which,
with but two or three exceptions, some apparent and others real, is
general: solids, liquids, and gases are expanded when their temperature
rises and are contracted when it falls. A given and invariable quantity
of matter of a certain substance corresponds in a particular thermic

condition to a determined
volume of the substance ;
hence it follows that varia-
tions of temperature can
be measured by variations
of volume or expansion.
Suppose that we take a
solid, liquid, or gaseous
body, and so arrange that
the quantity of matter of
which it is composed re-
mains invariable, or, if we
like, that its weight remains
always the same ; and that
we endeavour, when it is

heated or cooled, to mea-
sure either its volume or the
variations of its volume.
Now, these variations will
serve as measures of the
heating and cooling of the

wheneyer ft

FIG. 280. -Expansion of gases.

possesses the same volume, we shall be certain that it is in the same
thermic condition ; in a word, that it is at the same temperature.

The temperature of a body is, therefore, a particular state corre-
sponding to a determined volume of this body. It is said that the
temperature rises when the body gets warmer, and consequently, with
the exception of which we shall presently speak, when it is expanded ;
its temperature, on the contrary, falls if the body is cooled, and there-
fore diminishes in volume.

CHAP. I.]

THERMOMETERS.

421

ffl

fit

All instruments which indicate and measure the variations of their
own temperature, and, with more or less precision, those of the media
in which they are plunged, are called thermometers. Contrivances of
this kind are numerous, and we shall learn as we proceed that the
construction of some of them is based on other principles than those
of the expansion and contraction of bodies ; but the indications
which they give all relate to those of a thermometer which it is
convenient to take as a standard or type for all others. Y/e speak of
the mercurial thermometer, which we shall describe first.

The mercurial thermometer consists of a glass tube of very small
diameter, which is closed at one end and terminated
at the other by a spherical or cylindrical reservoh
(Fig. 281). The reservoir, and a portion of the tube
enclosing some perfectly pure mercury, together
with the rest of the tube, are entirely void of air
and every other gas. As the interior capacity ot
'she tube is only a very small fraction of the capacity
of the reservoir, the least variation of volume in the
latter is made apparent by a considerable change in
the height of the mercury in the tube. In order to
measure these variations, it is convenient to mark
on the tube of the thermometer two points which
correspond to two different temperatures, both fixed
and invariable, and to divide into a certain number
of equal parts the total increase of volume that
the mercury is subjected to on passing from the
lowest of these temperatures to the highest. As
experiment has shown that ice always melts at the
same temperature, and that the temperature of the
steam of boiling water is likewise constant when
the barometric pressure is at 760 mm. or 30 inches, these two fixed
temperatures are the most convenient to use as fixed points for the
graduation of the mercurial thermometer. The following is the
method by which this graduation is effected: —

The reservoir and part of the tube are plunged into a vessel filled
with pounded ice, and pierced with holes at the bottom, so that the
water which might acquire a higher temperature than that of the
melting ice can freely escape (Fig. 282). The level of the mercury

FIG. 281. — Reservoir
and tube of the mer-
curial thermometer.

422

PHYSICAL PHENOMENA.

[BOOK iv.

having become stationary, a line is marked on the stem : this point is
the zero of the graduation.

The thermometer is then placed in the position indicated in
Fig. 283, that is to say, in a bath where it is completely surrounded
by the steam of boiling water. The bath consists of a double
case of iron plates, wherein the steam circulates before escaping
into the air, so that the temperature of the internal space is not
modified by the exterior cold. Here again, when the mercury becomes
stationary, a second line is marked on the stem. At this point

(Fig. 283) the number 100 is marked,
if, as we have said, the barometric pres-
sure is at this moment at 760 mm.,1
which the manometer with bent limbs
(seen to the left of the instrument)
indicates.

If the interior of the tube is per-
fectly cylindrical, which must be
ascertained before blowing the bulb
of the thermometer, it is evident that,
if we divide the interval which sepa-
rates the zero of the melting ice from
the point 100, corresponding to the
temperature of boiling water, into 100
equal parts, each of these will indicate
equal capacities, and, when the level of the mercury traverses them
successively, equal dilatations of the liquid. These divisions, which are
called degrees, form the scale of temperatures, which can be extended
below 0° and above 100° for the measure of temperatures lower than
that of melting ice, or higher than that of boiling water. The divisions
are sometimes engraved on the tube, sometimes on a lateral tube
fastened to the thermometer tube, and sometimes again are marked
on the frame to which the instrument is fixed (Fig. 284).

1 If the barometric pressure is not 760 millimetres at the time of the experi-
ments, the level of the mercury will no longer indicate the fixed point where 100°
ought to be marked. It has been determined that the difference is a degree Centi-
grade (that is, the hundredth part of the dilatation between the point of fusion of
the ice and that of boiling water) for a pressure which differs 27 millimetres, more
or less, from 760, so that 101° must be marked if the pressure is 787 millimetres,
and 99° if, on the other hand, it is only 733 millimetres. Between these limits a
proportional correction is made for the excess or diminution of pressure.

FIG. 282. — Determination of the zero in the
mercurial thermometer; temperature of
fusion of ice.

CHAP. I.]

THEKMOMETEEiS

423

The Centrigade scale is not the only one which has been adopted
for the graduation of thermometers ; but it is the most generally
adopted, and the only one which is used at the present day in France
and in a great many other countries. Its invention is attributed to a

Pie. 283. —Determination of the point 100°, the temperature of boiling water, under a pressure

of 760 millimetres.

Swedish physicist, Andre" Celsius, who lived in the eighteenth century.
The scale of Ke'aumur divides the intervals between the same two
fixed points, melting ice and boiling water, into eighty degrees. A very
easy calculation converts Centigrade degrees into Reaumur's degrees ; it

424

PHYSICAL PHENOMENA.

[BOOK iv.

is sufficient to add to the first number its quarter : thus 28° E. equals
28° + 7° or 35° C. If we take a fifth from a Centigrade temperature,
we have the same temperature expressed in Ee'aumur degrees : thus,
35° C. = 35° - 7° or 28° E. ; 32° C. = 2o°-6 E. In Fahrenheit's scale,
which is used in Germany, England, and the United States, one of the
fixed points is that of boiling water, as in the preceding scales ; but
the other corresponds to a lower temperature than that of melting
ice, viz. that of a mixture of ice and salt. The zero is therefore
very low. Fahrenheit has marked the boiling point at 212°. As it
has been found that the temperature of melting ice corresponds to the
32nd degree of this scale, it follows that the hundred
degrees of the Centigrade scale are equivalent to
180 degrees Fahrenheit : hence the conversion of any
number of degrees from one of these scales to the
other becomes easy. If we wish to know, for ex-
ample, what is the equivalent of 120 degrees Fahren-
heit in Centigrade degrees, we begin by deducting 32,
which gives 88, of which the | is taken, the result
being 46° 66 C. On the other hand, having the tempe-
rature 45° C. to convert into divisions of Fahrenheit's
scale, the J are taken, which gives 81°F. above melt-
ing ice ; this is marked 32°, as we have before seen :
81° + 32° or 113° F: thus becomes the result of the
conversion.

Delisle's scale is also used, principally in Eussia :
the boiling point is marked 0°, and the melting point
of ice 150°. Nothing is more simple than to con-
vert a temperature marked on this scale into any of
the three others.

Care must be taken, when a temperature is stated,
according to one or other of the graduations, to indicate whether it
is higher or lower than that marked by zero. Physicists do this by
considering temperatures higher than 0° as positive and placing the
sign + before them, and temperatures lower than 0° as negative,
distinguished by the sign — . These conventionalities once adopted,
similar rules to those of the positive and negative algebraic quantities
apply for operations effected on numbers expressing temperatures
where they are combined by means of addition and subtraction.

FIG. 284.— Centigrade
thermometers with
their graduated
scales.

CHAP. I.]

THERMOMETERS.

425

But it is necessary to give to each
of these numbers its true meaning,
and to abstain from attributing to
it an absolute value which it does not
possess. Thus we can only say, that
a temperature is double or triple of
another, or at least, if we use these ex-
pressions, nothing must be inferred as
to the quantities of heat which corre-
spond to them. This simply signifies
that the expansion of the mercury
above the fixed starting-point, or zero,
is in this case double or triple of the
total expansion corresponding to the
second elevation of temperature. In a
word, we must not forget that the unit
of temperature — for instance, the centi-
grade degree in the centesimal scale —
represents only an expansion of the
mercury contained in the reservoir of a
thermometer, equal to the hundredth
part of the total dilatation which the
same liquid would undergo on 'passing
from the temperature of melting ice to
that of boiling water.

The thermometer which we have
just described is based on the expan-
sion of mercury, that is to say, of a
liquid contained in a glass envelope.
But when, by a variation of tempera-
ture, the volume of the liquid changes,
the capacity of the envelope changes
also. If these expansions or contrac-
tions of the mercury and the glass
were equal, as they are made in the
same direction, the level would not
vary, and therefore it would give no
indication. In reality, mercury expands

I x

FIG. :!&>.— Tlicriuoiiiutricul scales.

426 PHYSICAL PHENOMENA. [BOOK n.

seven or eight times more than glass, and this fact renders the mercurial
thermometer possible. But from this we learn that it is not the
expansion of the mercury which causes the level to vary, but the
difference between the expansions of the liquid and that of the enve-
lope; in a word, it is the apparent dilatation of the mercury, not its
absolute dilatation. But it is no less evident that the different ther-
mometers, constructed and graduated as we have just stated, must
always be comparable between themselves, whatever the dimensions
of the tubes and reservoirs and the quantity of mercury in each of
them. Only, as different kinds of glass are not equally expansible,
especially at high temperatures, in order that there should be cor-
respondence between the indications of the instruments submitted
to the same conditions, it is necessary that they be made of glass
having the same composition.

The sensibility of a mercurial thermometer, that is to say, the
rapidity with which it assumes the temperature of the surrounding
medium, is greater as the mass of mercury in the reservoir is less, and
as the surface of the envelope is greater. In order to fulfil this second
condition in the best manner, the cylindrical or even spiral form is
given to the reservoir, as it is preferable to a spherical bulb. This
kind of sensibility is especially desirable for ascertaining variations
of temperature which quickly succeed each other. There is another
kind of sensibility no less useful than the first: it is that which
allows very slight variations of the level, corresponding to very slight
variations in the temperature, to be manifested, so as to allow the
indication of the smallest fraction of a degree. This quality is ob-
tained by giving larger capacity to the reservoir, and small diameter
to the tube, so that for the expansion indicated by one degree the
level varies considerably. Mr. Walferdin has constructed thermo-
meters, to which he gives the name of melastatic, in which the
hundredth part of a degree can be detected : whenever these instru-
ments are used, it is necessary, on adding or taking away from the
mercury, to regulate their course for the variations of temperature to
be ascertained. The mercurial thermometer cannot be employed for
temperatures higher than 360° above zero, because at this point
the liquid boils and would break the tube. In like manner, below
— 35° or — 36° the mercury is near the temperature at which it
solidifies, and then contracts irregularly, so that it would furnish

CHAP, i.] THERMOMETERS. 427

inexact indications. Beyond either of these two limits, thermometers
of a different kind, which we shall briefly describe, are employed.

Let us commence with the alcohol thermometer, which is used to
measure very low temperatures. This instrument does not differ in
form from the mercurial thermometer; but it is graduated by com-
parison with a standard mercury thermometer, that is to say, the
two tubes are plunged simultaneously into baths, the temperature of
which is made to vary. The points at which the level of the alcohol
becomes stationary are marked for each temperature which is deter-
mined from the mercurial thermometer, and the intervals are divided
into as many equal parts as there are degrees from one to the other.
But even with these precautions, it is seldom that alcohol thermo-
meters agree between themselves, or with
the standard thermometer, which is explained
by the irregularity of the expansion of this
liquid at different temperatures. For lower
temperatures than that of melting ice, it
would be preferable to use thermometers
filled with common ether, as this dilates with
much greater regularity than alcohol.

Thermometers are also constructed of gas,
based for example on the expansion of air.
Fig. 286 represents two of these instruments,
the first that were invented for the measure-
ment of variations of temperature. Galileo
invented the first: it consists of a tube and FlG. 286.-Air thermometers of

, ,, ,. ., , Galileo and Cornelius Drebbel.

reservoir, enclosing a small liquid column or

index, A, which separates the air of the reservoir from the outer air ; as
the temperature increases, the air contained in the bulb of the thermo-
meter is warmed, dilates, and forces the index towards the open end of
the tube. The other instrument is also formed of a tube and reservoir
similar to the first, but its open end is immersed in a liquid contained
in an open vessel ; by cooling, the air decreases in volume, and its
elasticity becomes less, so that the liquid, which is always submitted
to the exterior atmospheric pressure, rises to a greater or less
height in the tube. This instrument, which was much in request
during the last century, was invented by a Dutchman named
Cornelius Drebbel. These two thermometers are now graduated by

428 PHYSICAL PHENOMENA. [BOOK iv.

comparison with a mercurial thermometer. The points are marked at
which the liquid becomes stationary at two different temperatures,
and the interval is divided into as many equal parts as it comprises
degrees. But they are both also affected by changes of atmospheric
pressure, and are therefore not capable of much precision ; their chief
value consists in the rapidity of their indications.

Leslie and Eumford invented two thermometers based on the
expansion of air; but not possessing the same inconveniences as
the preceding ; in other words, they are uninfluenced by pressure.

FIG. 287.— Differential thermometers of Leslie and Eumford.

They both consist of a tube, bent twice at a right angle, and ter-
minated at each extremity by a bulb or reservoir. In Leslie's ther-
mometer (Fig. 287) the tube encloses a column of sulphuric acid
coloured red ; the level is the same in each limb, when the tem-
perature of the two bulbs is equal ; this common level is marked
0. If now one only of the reservoirs is warmed, the air which it
contains, in expanding, presses against the liquid ; the level of the
corresponding limb falls to I, whilst it rises in the other to a ; and
the height above zero marks the differences of temperature of the
reservoirs, if this instrument has been graduated by comparison with
a mercurial thermometer.

Eumford's air thermometer differs from the preceding, inasmuch

CHAP, i.] THERMOMETERS. 429

as the liquid column is replaced by an index which occupies the
centre of the horizontal portion of the tube, when there is equality of
temperature between the two reservoirs. If one of these is warmed
more than the other, the expansion of the air causes the index in the
horizontal part of the tube to move towards the colder bulb, and the
difference of the temperature is measured by the number of divisions
which this index passes over from zero.

These two instruments thus mark differences of temperature, and
they are therefore known as differential thermometers. But they can
also indicate absolute temperatures, if the graduation has been effected
with this object in view.

The expansion of solid bodies may also be employed to measure
temperatures. The instruments which we have described above
are based on the unequal expansion of liquids, gases, and of the

FIG. 288.— Unequal expansion of two different metals for the same elevation Of temperature.

vessels which contain them ; this inequality, perceptible in liquids,
becomes considerable in gases. The construction of the metallic
thermometers represented in Figs. 289 and 290 depends on the
inequality of expansion of different solid bodies. Two metallic
plates — for example, one of copper and the other of zinc sol-
dered together lengthways, so as to form a straight bar, expand
unequally when the temperature is raised ; the bar then bends, as in
Fig. 288 ; the zinc, which is the more expansible of the two metals,
forms the convex side, and the copper the concave. When the bar
has returned to its primitive temperature, it assumes its rectilinear
form, to bend again in the contrary direction if it is afterwards
subjected to cooling.

430

PHYSICAL PHENOMENA.

[BOOK iv.

The metallic dial thermometer (Fig. 289) is composed of a curved
plate of copper and steel soldered together ; one of the extremities of
this is fixed, while the other is supported by the small arm of a
lever, the large arm of which, in the form of a toothed sector, works
in the pinion of an index. Variations of temperature increase or
diminish the curvature of the plate, and thus cause the lever and
consequently the index to move, sometimes in one direction and some-
times in the other. The dial is divided into degrees, by observing the
indications of a mercurial thermometer. In Bre'guet's metallic ther-
mometer (Fig. 290) the plate is formed of three ribbons of silver, gold,
and platinum, soldered together and formed into a spiral : the silver,
being the most expansible of the three metals, forms the inner surface
of the spiral. This is suspended vertically, and its lower extremity

FIG. 289.— Metallic dial thermometer.

FIG. 290.— Breguet's metallic thermometer.

supports a horizontal index, which moves over the divisions of the
dial. When the temperature rises, the curvature of the spiral
diminishes under the influence of the greater expansion of the silver,
and the needle moves in one direction : it moves in the contrary
direction if the temperature falls. As the bulk of the spiral is
extremely slight, it very rapidly acquires equilibrium of temperature
with the surrounding air. Breguet's thermometer is therefore very
sensible, and useful for noting rapid variations of temperature.

We can only allude to pyrometers, instruments which are used for
measuring very high temperatures, such as those of blast-furnaces,
forge-fires, &c. ; some are based on the expansion of solids, others on
the contraction of clay. The trials which have been made in order to

CHAP, i.] THERMOMETERS. 431

compare the indications of pyrometers with those of mercurial
thermometers have not given very accurate results. When great
precision is desired, air pyrometers are used for measuring high
temperatures, a description of which will be found in more detail
in many treatises on Physics.

The various thermometers which we have recently described
determine the variations of their own temperature, by the different
expansions and contractions of their own substance. But the object
which is proposed in constructing them is to measure the temperature
of various media, whether solid, liquid, or gaseous — which in each
instance requires particular precautions.

If it is a question of the temperature of the air or a gas, or
again of a liquid, the thermometer is immersed in it; and if the
instrument be of great sensibility, if its mass be very small in com-
parison with that of the medium, the temperature indicated by the
thermometer, when the level of the mercury or the index is at rest,
may be taken without sensible error for that of the medium itself.
If it is a question of a solid body, a cavity large enough to receive the
reservoir of the instrument is made, or, still better, this cavity is filled
with mercury ; after a short time, the temperature of this liquid is in
equilibrium with that of the body, and the thermometer is then
immersed. It is always necessary that the mass of this . be very
small compared with that of the body ; indeed, as there is exchange
of heat between them, the indication no longer relates to the original
temperature of the body, but to that which is established at the
end of this change, and on the hypothesis that the mass of the
instrument is very large, the difference would be considerable.
Hence it is evident, that this cause of error can never be entirely
avoided ; the effects can only be lessened, in order that the result
may not be perceptibly altered.

432 PHYSICAL PHENOMENA. [BOOK iv.

CHAPTEK II.

MEASURE OF EXPANSION.

Effects of variations of temperature in solids, liquids, and gases — Applications to
the arts — Eupert's drops — Measure of the linear expansion of solids — Expansion
of crystals — Contraction of iodide of silver — Absolute and apparent expansion
of liquids — All gases expand to the same extent between certain limits of
temperature.

A BODY expands when its temperature increases : this is the
universal fact which we have stated, and which is employed
to measure changes of temperature. But to what extent does the
volume increase, and by what fraction of the primitive volume
is it increased for one degree of the centigrade thermometer ?
Does this fraction vary in different substances, and does it remain
the same at every temperature ? Such are the questions which
naturally present themselves to physicists when they have deter-
mined by observation the effects of variation of temperature. Before
indicating the results at which they have arrived, let us show by
a few examples the practical utility of the precise knowledge of
these effects, and the necessity which often arises of correcting
or foreseeing them.

If a fragile body which is a bad conductor of heat is subjected
to quick changes of temperature, the effect produced will be the
breaking of the body. Thus, if a red-hot bar is placed on a piece of
cold glass the glass cracks ; the same thing happens with a piece of
very hot glass if it is suddenly placed in contact with a piece of
cold iron. In the first instance, sudden expansion is produced in the
portions of the glass touched by the hot iron, and the surrounding
portions, which have not had time to become warmed, break violently
from the first — hence the rupture. In the second instance, on the

CHAP, ii.] MEASURE OF EXPANSION. 433

other hand, the portions first touched are contracted before the
other parts have had time to cool, and rupture is again the conse-
quence of this sudden molecular movement. We all know that
boiling water cannot be poured into a cold glass vessel without
breaking it by the quick expansion of the sides in contact with the
liquid.

During hot summers the expansion of metals used in buildings
and their contraction by cold in winter, produce effects which are
the more apparent when these metals are united to materials whose
expansibility differs from their own. The following is a curious
example, quoted by Tyndall in his work on Heat, the observation
and explanation of which is due to Canon Moseley: — "The choir
of Bristol Cathedral was covered with sheet lead, the length of the
covering being sixty feet, and its depth nineteen feet four inches.
It had been laid on in the year 1851, and two years afterwards
it had moved bodily down for a distance of eighteen inches. The
descent had been continually going on from the time the lead had
been laid down, and an attempt to stop it by driving nails into
the rafters had failed; for the force with which the lead descended
was sufficient to draw out the nails. The roof was not a steep
one, and the lead would have rested on it for ever, without sliding
down by gravity. What then was the cause of the descent ? Simply
this. The lead was exposed to the varying temperatures of day and
night. During the day the heat imparted to it caused it to expand.
Had it lain upon a horizontal surface, it would have expanded
all round ; but as it lay upon an inclined surface, it expanded
more freely downwards than upwards. When, on the contrary,
the lead contracted at night, its upper edge was drawn more easily
downwards than its lower edge upwards. Its motion was therefore
exactly that of a common earthworm: it pushed its lower edge
forward during the day, and drew its upper edge after it during
the night, and thus by degrees it crawled through a space of eighteen
inches in two years."

From this example we learn how important it is to note the
changes of volume in solids which are used in building or the arts.
Railway lines lengthen in summer and shorten in winter; it is
necessary, therefore, on laying them, to give them a certain play
which allows the lengthening to take place freely, otherwise the

L L

434

PHYSICAL PHENOMENA.

[BOOK iv.

heat would force the bolts from the sleepers, or would contort
the line. The damaged line which occasioned the Fampoux accident
011 the Northern Railway of France was apparently caused by a
contortion of this nature, as the ends of the rails had not a sufficient

interval between them. ,

Stones held together by iron clamps are often broken, either by
the expansion or contraction of the metals, both being greater than
that of the stone. The force with which the molecules of bodies
are sometimes separated and sometimes drawn together, one against
the other, by change of temperature, is enormous. A bar of iron a
metre (39'3 inches) long expands lengthways 1*17 mm., when its tem-
perature is raised from 0° to 100° ; it contracts to the same amount
in passing from 100° to 0°. Now, it has been calculated that in order

to overcome this molecular
movement, a force equal to
the pressure of 2,450 kilo-
grammes— 5,000 Ibs. — must
be employed, if the section of
a bar of iron is a square cen-
timetre— six to the square
inch — and 245,00-0 kilo-
grammes if the section is a
square decimetre. This force
has been employed for the
holding together of the lateral
walls of a gallery in the Con-

FIG. 291.— Boom of the Conservatoire des Arts et Metiers. Servatoire deS Artset Metiers,

which the pressure of the

roof had driven out of the vertical. Two bars of iron were placed so
as to cross the two walls at the upper part ; they were terminated on
the outside by screws furnished' with nuts. The whole of their
length was quickly heated, which produced a lengthening, and the nuts
were then screwed up close against thick pieces of wood placed on the
outside of the roof walls whilst the bars were still hot. On cooling,
the bars contracted, and by degrees the force of contraction drew
the walls nearer together. By repeating the same operation several
times they were at last brought to a vertical position.

Cartwrights utilize the contracting force of cooling iron to bind

CHAP. n.J MEASURE OF EXPANSION. 435

together the spokes of carriage wheels. The iron tire is forged in
such a way as to surround the wood, when it is heated to rather
a high temperature ; on cooling, it binds the parts of the wheel
strongly together.

Dutch tears, or Kupert's drops, are drops of melted glass which
have been suddenly solidified in cold water. On breaking the fila-
ment of glass with which they are terminated, the whole mass
instantly becomes powder, with such a force that if the drop has
been previously plunged into a flask filled with water the shock
transmitted to the water is sufficient to break the flask. A similar
effect is produced in very thick glass flasks which have been cooled
suddenly after having been blown. A grain of sand thrown into
the vessel is sufficient to cause the bottom to fall
out (Tyndall). The cause of this is the same in this
last example as in the Dutch tears. The exterior
of the glass drops cools first, imprisoning the in-
terior mass, which has not yet solidified; when
this cools in its turn, it contracts, and the effect
of the contraction being exercised evenly on the
outer envelope, it remains in equilibrium. But
the molecules are in a state of violent tension,

, ,, . , , , ., . FIG. 292.— Dutch tears.

and the least rupture suddenly destroys the

equilibrium in one point, and at the same time destroys it in the

whole mass.

The expansion of liquids is generally greater than that of solids,
and the expansion of gases is the greatest of all. We have seen
how this is proved ; it now remains for us to show by what means
the expansions are measured, by what methods the so-called co-
efficient of expansion of a solid, liquid, or gas is determined. The
unit of volume of the body being given, let us imagine that the
temperature is raised one degree centigrade : expansion or increase
of vol ume will of course result. This increase, expressed in numbers
referred to this same unit, constitutes the co-efficient of expansion
of the substance for the temperature employed. In a more general
sense, we may say that it is the fraction of the primitive volume
added to the volume of any body when its temperature is raised
one degree. Thus a litre or cubic decimetre of mercury heated from
0° to 1° becomes a litre plus 179 millionths, or 1 -0001 79 decimetre,

L L 2

436

PHYSICAL PHENOMENA.

[BOOK iv.

The fraction 0 000179 is the co-efficient of expansion of mercury at
zero. The numbers of which we here speak vary with the nature
and physical condition of the substances. Moreover, the co-efficient
of expansion of one body generally varies for different degrees of
the thermometric scale, even when its physical condition does
not change.

In liquids and gases the cubic expansion, or expansion of volume,
is considered ; but in solids it is possible to determine the increase
of one of the dimensions, that is to say, the linear expansion, or,
in the case of two dimensions, superficial expansion. As a solid
of any form generally expands equally in every direction, so as to
retain its original form at all temperatures, the increase of its volume
can be deduced from that of one of its dimensions; besides, it is
proved that the co -efficient of cubic expansion is perceptibly to
all intents and purposes triple of the co-efficient of linear expansion ;
for this reason, in the case of solid bodies, this last co-efficient is
alone determined.

FIG. 293.— Measure of the linear expansion of a solid, by the method of Lavoisier and Laplace.

Let us now consider the nature of the method devised by
Lavoisier and Laplace for measuring the linear expansion of a
solid bar. The bar A B is fixed at A, so that it can expand only at
the extremity B ; on expanding through the space B B' it forces the
rod OB, which is fixed and can revolve on the point o, into the
position OB'. The telescope LL, originally horizontal, moves with
the rod to L'L, so that, in place of being opposite the point c of
the vertical scale C (/, it is then opposite c'. By this means they
substitute for the difficult measure of the smaller space B B' that
of a space c c', the ratio of which to the space B B', through which

CHAP. If.]

MEASURE OF EXPANSION.

437

the rod has expanded, is equal to the ratio of o c to OB. Fig.
294 shows the arrangement of the apparatus employed in the
preceding method. The metallic bar s, whose expansion is to be
measured, is immersed in a trough filled with water, beneath which
is placed a fire to raise the temperature ; at one end it is in contact
with a fixed glass rod B', immovably fixed to the pillars; at the
other end it presses against the movable glass rod B, which com-
municates its motion to the telescope. The water in the trough
being first at 0°, the observers note the division of the scale with
which the micrometric wire stretched horizontally across the field
of the telescope corresponds. Then, after having replaced the iced
water by water raised to a temperature of 100° — that is, to the boiling

PIG. 294. — Laplace and Lavoisier's instrument for the measure of linear expansion.

point — the division of the scale is again observed. By a simple pro-
portion the relation of the elongation of the bar to its original
length is determined; in other words, the expansion for 100° of
temperature.

Operating thus on solid bars of different substances and between
different limits of temperature, Laplace and Lavoisier determined,
for the co-efficients of expansion of solids, numbers which vary
for different substances, but which are sensibly constant for the
same substance for the different degrees of the thermometric scale,
between the temperatures 0° and 100°. The following are some of the

438 PHYSICAL PHENOMENA. [BOOK iv.

results determined by various observers either by the method just
described or by other processes.

Iron. . . ...... ,,.,.... 0000012

Copper 0-000017

Tin 0-000022

Lead .' 0-000029

Zinc OO00032

Silver , 0-000019

Gold 0-000015

Platinum G'000009

Steel 0-000011

Aluminium 0'000022

Bronze 0-000019

Wood charcoal O'OOOOll

Granite 0'000009

White marble 0 '000008

Building stone 0'000009

Glass , 0-000008

Ice • . , 0-000053

The preceding co-efficients of expansion apply only to the speci-
mens which were used to determine them; according to some
observers, the same substances are found to possess totally dif-
ferent co-efficients, dependent on the particular molecular conditions
in which the substances used by each of them exist. Thus, wrought
iron, iron wire, and cast iron have not the same co-efficient of ex-
pansion ; and a similar remark applies to other metals. Solid bodies
which have not a homogeneous structure in every direction expand
unequally in different directions. Thus the expansion of dried wood
is not the same in the direction of the fibres and perpendicular
to their direction. All doubly- refracting crystals have unequal
co-efficients of expansion in different directions. According to
Mitscherlich and Fizeau, there are even some which, when they in-
crease in length by heat in one direction, contract in another. Such
is carbonate of lime or Iceland spar : for while, on raising the
temperature one degree, this crystal expands 29 millionths in the
direction of the optical axis, it contracts perpendicularly to the
axis, and this contraction amounts to nearly 6 millionths. A similar
phenomenon is observed in the emerald and in orthic feldspar.
The differences of crystalline structure in different directions,
which we have seen indicated in those substances by the curious

CHAP, ii.] MEASURE OF EXPANSION. 439

effects of double refraction, are here shown under another form
which is not less interesting.

Moreover, as we have just stated, these anomalies are not real
exceptions to the law of expansion of solids by heat, because when
the whole expansion is considered there is increase of volume.
This is not the case however with iodide of silver. From some
very interesting researches by M. Fizeau on this substance, it
appears that it undergoes a real contraction in proportion as it
increases in temperature between limits rather extensive, since they
embrace 80 degrees of the thermometric scale ; and further, that
the co-efficient of contraction — which physicists call the negative
co-efficient of expansion — becomes greater as the temperature in-
creases.

For some time it was believed that ice or solidified water was
contracted by an elevation of temperature, thus forming an ex-
ception to the general phenomena of expansion of solids : this how-
ever is not the case, and Brunner found that its density increased
with the fall of temperature. The co-efficient of expansion of ice,
as we have seen in the table at page 438, rises as high as 53 ten-
millionths, higher, in fact, than that of zinc, the most expansible
of all metals. Wood, and the greater number of organic substances,
diminish in volume when they are warmed, if they are not com-
pletely desiccated ; but this is only an apparent exception. Heat
induces evaporation of the water which these bodies contain, and
in diminishing in volume they also lose in weight ; besides, on
returning to their original temperature by cooling, they do not re-
sume their primitive volume. Clay, although completely dried, also
contracts when it is submitted to an increasing temperature, and it
is on account of this property that clay pyrometers have been
constructed ; these instruments indicate the temperature of large
kilns : but it has been proved that the contraction is owing to the
commencement of vitrification or chemical combination of the ele-
ments of the clay ; besides which, on cooling, the clay no longer
assumes the former volume.

The expansion of liquids is greater than that of solids. We
have already seen that the construction of ordinary thermometers
is based on the difference of the expansion of glass and mercury.
As the liquids, the expansion of which we desire to measure,

440 PHYSICAL PHENOMENA. [BOOK iv.

are necessarily enclosed in solid vessels or envelopes, which them-
selves change in volume when the temperature is changed, it
follows that we must distinguish between absolute expansion,
that is to say, the real increase of volume of the liquid, and
apparent expansion, as it is observed by the aid of a thermometric
tube divided into parts of equal capacity. The absolute expansion
of a liquid is evidently equal to its apparent expansion, plus the
expansion of the envelope.

The following is the process employed for the measurement of
the absolute or real expansion of liquids. The absolute expansion
of mercury was first determined by a process which we cannot here
describe; then, on subtracting from the number found the apparent
expansion of the same liquid, the expansion of the glass was
obtained. This being once known, the expansion of any liquid
can be deduced from it by a reverse operation, that is to say, by
first measuring the apparent expansion and adding to it the
expansion of the glass or envelope.

Kesults have shown that liquids not only expand more than
solids, but that these co-efficients of expansion — this refers to cubical
expansion — are not constant. Let us take some examples.

M. Kegnault, by perfecting the method invented by Dulong
and Petit, has obtained the following numbers, which represent
the co-efficient of absolute expansion of mercury, for an elevation
of one degree centigrade: —

Co-efficients of cubic
expansion of mercury.

Mean between 0° and 100° 0*00018 170

at 100° 0-00018305

at 200° 0-00018909

at 300° 0-00019413

at 350° 0-00019666

We perceive that the co-efficient increases with the temperature,
but between 0° and 100° it is sensibly constant, and then equal
to -g-eVrj- ; while at 0° it is TVST* Such is the fraction by which any
volume of mercury expands at the temperature indicated.

Water and alcohol expand more than mercury between 0° and
the temperatures 100° and 80°, which are their boiling points.
Moreover, the former of these liquids offers an anomaly which deserves
attention. Between the temperature of melting ice and 46, water,

CHAP. II.] MEASUEE OF EXPANSION. 441

instead of expanding, diminishes in volume ; at this temperature
it attains its maximum density. Heated above 4° it continues
to expand till it reaches 100° C. M. Despretz, who has made
a complete study of the expansion of water and its contraction
near 0°, has given the following volumes and densities of water
at different temperatures: —

Temperatures. Volumes. Densities.

0° 10001269 0-999873

1° 1-0000730 0-999927

2° 1-0000331 . . . . . 0-999966

3° 1-0000083 VW , . 0-999999

4° 1-0000000 .... . 1-000000

5° 1.0000082 ..-.--.-. 0-999999

6° 1-0000309 &v.j . . . 0-999969

7° 1-0000708 ... , ... . 0-999929

8° 1-0001216 . . *.'.". 0-999878

100° 1-0431500 0-958634

The contraction of water heated from 0° to 4° can be proved very
simply. A cylinder of glass, full of water at a temperature above
4° C., is surrounded, midway between the
top and bottom, by a tray containing ice.
The upper stratum of water gradually and
continuously cools, and the thermometer
which is immersed in it falls from 4° to 0°,
whilst the lower thermometer, after having
fallen to 4°, remains stationary. This ex-
periment proves that the upper stratum on
cooling to 4°, becoming heavier than the
lower ones, falls to the bottom of the glass FlG. 295.__Expe^pTving the
vessel, and is replaced by those, which are contraction of wate
in turn cooled down by the ice. But when the temperature is lower
than 4°, the water remains at the upper part, as the indications of
the two thermometers prove.

Gases expand much more than solids and liquids under the action
of heat : a thin glass sphere, or a balloon of gold-beater's skin filled
with air, or any other gas, bursts when it is slightly heated. As
according to Mariotte's law, the volume of a gas is changed by
pressure, it is necessary, in order that its co-efficient of expansion,
may possess a definite value, that care be taken to indicate to what

M M

442 PHYSICAL PHENOMENA. [BOOK iv.

pressure it has been submitted. These co-efficients are ordinarily
taken at an atmospheric pressure of 760 mm. Gay-Lussac determined
a great number for temperatures comprised between 0° and 100°, and
arrived at the remarkable result, that the co-efficient of expansion
is the same for all gases, simple, mixed, or combined. According
to this illustrious physicist, a volume of gas, on being heated
1° C., increases the 267th part of its volume : a cubic decimetre
of air, passing from 0° to 100°, therefore expands 375 cubic centi-
metres, that is, more than a third of its volume at 0°. The number
which we have just mentioned is a little too high, as the beautiful
researches of M. Eegnault have proved ; and he has at the same time
shown that Gay-Lussac's law is not absolute. Air, nitrogen, hydrogen,
and carbonic oxide have nearly the same co-efficient of expansion,
which is 0*00366, which is equal to the fraction ^T. But those of
other gases are different : thus, in the case of cyanogen, it is equal to
0 '00388, or to the fraction ¥|g-. Moreover, the less the pressure to
which the different gases are submitted, the more do their co-
efficients of expansion approach equality; thus verifying Gay-
Lussac's law.

We shall see hereafter that the expansion of air and gases by heat
explains many meteorological phenomena. It is also the principle
of numerous applications, among which we may quote air balloons,
hot-air stoves, and hot-air engines.

CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE. 443

CHAPTER III.

EFFECTS OF VARIATIONS OF TEMPERATURE : CHANGES IN
THE STATE OF BODIES.

WE all know that a mass of water which is liquid at certain
temperatures is capable of passing into the solid state when
its temperature falls below a certain limit ; in a word, it becomes a
piece of ice without changing its nature, that is to say, without
ceasing to be formed of the same chemical elements. On returning
to its original temperature, it again resumes the liquid condition ;
and if it is then heated to 100°, under an atmospheric pressure of
760 mm., it is converted into vapour. The greater number of liquids
are like water in this respect, and can exist in either the solid,
liquid, or gaseous condition.

Bodies which are solid at ordinary temperatures, metals for
example, change their condition when they are submitted to a
sufficiently intense heat; they are then liquefied, and sometimes
vaporized. Cooling produces opposite phenomena, and causes a gas
to pass into a liquid, and then into a solid.

These various changes of condition are effected under circum-
stances which vary with the nature of the substance, but which
nevertheless conform to certain common laws, which we shall now
discuss. First, however, let us enumerate the changes of condition

M M 2

444 PHYSICAL PHENOMENA. [BOOK iv.

in solids, liquids, and gases, which can be produced under the
influence of variations of temperature.

An increase of temperature produces, in solids, a change to a
liquid state, which is called fusion ; in liquids, it gives rise to a
gaseous state, or vaporization : we shall see, further on, the distinction
which must be made between vaporization and evaporation, which
also designates the change of a liquid into gas, or into vapour.

Cooling causes gases to become liquid : this is liquefaction ; and
in liquids, a return to the solid state, which is sometimes called
solidification, and sometimes congelation or freezing.

The fusion of solid bodies takes place at temperatures which
differ from each other considerably. Thus, whilst ice melts at 0°,
sulphur at 125°, and lead at 322°, a temperature of 1,500° is neces-
sary to melt iron, and nearly 2,000° to melt platinum. But all solids
have this common property, that the temperature of fusion is definite
for each of them; moreover, during the time that the change from
the solid to the liquid condition is taking place, the temperature of
the mass remains the same, whatever may be the intensity of the heat
which produces the fusion. We may remember that it is this property
which has been utilized in determining a fixed point of the thermo-
meter. The only effect which is produced by an increase in the energy
of the source of heat is a greater rapidity in the fusion of the
solid.

The passage to a liquid state of the greater number of solids is
made suddenly; thus ice, sulphur, and metals assume their fluidity
in a moment. Other substances, on the contrary, begin by being
softened ; and they become viscous, before becoming quite fluid.
Glass affords an example of this condition, which gives great facility
to its working, and enables it to be blown and worked into various
forms.

Formerly we were not able to produce a temperature sufficiently
high for the fusion of certain bodies : hence they were called refrac-
tory or fixed. In the present day the number of these substances
is considerably diminished, and the fusion of numerous rocks, which
used to be considered infusible, has been effected. M. Despretz has
even succeeded in producing an incipient fusion in charcoal, the most
refractory of all known bodies. Other solids are infusible, because
heat decomposes them ; such are chalk, pit-coal, and marble : never-

CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE. 445

theless, by enclosing a piece of marble in an iron cylinder, hermetically
closed, and then submitting it to a high temperature, a certain portion
of this body can be fused. The heat at first decomposes part of
the marble into carbonic acid and lime, and the gas, by its elastic
force, prevents the continuance of decomposition, and the remaining
marble is partially fused.

The expansion which a solid body undergoes when submitted to
increments of heat, generally continues until the commencement of
fusion ; at this juncture it takes place still more rapidly, so that the
liquefied mass has a greater volume than that of the solid which
produced it. There are some exceptions to this law, and we shall
have occasion to return to this subject in speaking of the solidifica-
tion of liquids. A foreseen relationship exists between the latter
phenomenon and that which we have just studied : for they are
both effected for the same substance, at a fixed temperature : in a
word, the point of solidification is the same as the point of fusion.
Thus, water becomes ice when its temperature reaches 0°; lead is
solidified when cooled to 322°, sulphur to 115°, iron to 1,500°,
platinum to 2,000°. And we have another similarity in the fact
that the temperature of the liquid mass remains constant during
the whole time of solidification; a more intense removal of heat
renders the passage to the solid state more rapid, but it does not
lower the temperature of the mass.

The term congelation or freezing is more particularly applied to
solidification which takes place at a low temperature, — for example,
below 0°. Water congeals at 0°, mercury at 39° below 0° ; many
liquids, such as bisulphide of carbon and alcohol, have not yet
been solidified, although by using refrigerating mixtures their tem-
perature has been lowered to 80° below 0°.

We thus see that the temperature of the fusing point of solids is
the same as the temperature of solidification. Nevertheless it is
possible, under certain circumstances, to lower the temperature of a
liquid mass below this point without producing solidification. Water,
for example, when enclosed in a vessel and sheltered from the agita-
tion of the air, can remain liquid at a temperature 20° below 0°. In
this experiment it must be very limpid, in order that it may be kept
at perfect rest, and the cooling must be effected gradually. But when
it is in this condition, the slightest agitation, or the throwing in of a

446 PHYSICAL PHENOMENA. [BOOK iv.

small piece of ice, is sufficient to cause congelation to take place
instantly throughout the whole mass. Then a remarkable result
occurs, for there 'is a disengagement of heat, and freezing takes place
at a temperature of 0°, as under ordinary circumstances.

A solid, on melting, expands quickly, and the reverse phenomenon
ought to take place when a liquid mass is solidified. Experiment,
indeed, has shown that there is a diminution of volume. But this
is not a general law, as there are exceptions, such as water, cast-iron,
bismuth, and antimony. These substances expand on solidifying,
and this property is utilized in the arts, in the case of molten iron,
and allows the reproduction in a very perfect form of the interior of
the moulds in which this substance flows.

We have already learnt that water expands on cooling from 4°
to 0°, so that the sudden expansion which it undergoes on congealing
appears to be the continuation of the same phenomenon, and renders
the explanation which is given to it probable : the phenomenon is
explained by the new disposition which the molecules take in the
vicinity of the point where this crystallization is effected. When the
passage to the solid state is effected, the expansion is sudden, and is
performed with an irresistible force, as shown, by the following experi-
ment, the description of which we take from Tyndall's " Treatise on
Heat :" — " But to give you an example of this energy, a quantity of
water is confined in this iron bottle. The iron is fully half an inch
thick, and the quantity of water is small, although sufficient to fill
the bottle. The bottle is closed by a screw firmly fixed in its neck.
Here is a second bottle of the same kind, prepared in a similar
manner. I place both of them in this copper vessel, and surround
them with a freezing mixture. They cool gradually, the water within
approaches its point of maximum density ; no doubt at this moment
the water does not quite fill the bottle, a small vacuous space exists
within. But soon the contraction ceases, and expansion sets in ; the
vacuous place is slowly filled, the water gradually changes from
liquid to solid ; in doing so it requires more room, which the rigid
iron refuses to grant. But its rigidity is powerless in the presence
of the atomic forces. These atoms are giants in disguise, and the
sound you now hear indicates that the bottle is shivered by the
crystallizing molecules, — the other bottle follows, and here are the
fragments of the vessels, showing their thickness, and impressing

CHAP. III.

EFFECTS OF VARIATIONS OF TEMPERATURE.

447

you with the might of that energy by which they have been
thus riven."

Two bombs filled with water, the fusee holes being closed firmly
by an iron stopper, were exposed to intense frost : in one instance
the stopper was projected to a distance of 500 feet on freezing,
and a long cylinder of ice issued from the opening (Fig. 296) ; the
other bomb was split open, and a sheet of ice was forced through
the crack. This experiment is given in M. Daguin's "Traite" de
Physique," and was made by Major Edward Williams, of the Artillery
in Quebec.

FIG. 296. — Effects of expansion produced by the freezing of water.

Similar results have been obtained with bismuth. An iron bottle
rilled with melted metal, and closed with a screw-stopper, bursts when
the metal begins to solidify ; the rapid expansion which determines
the changes of condition develops an expansive force so considerable
that the envelope cannot resist it, and is broken.

The expansion of water at the moment of congelation explains
the bursting of water-pipes during a frost ; the accident is not per-
ceived until a thaw, because as long as the water remains as ice in
the pipes no escape can be manifested, but when the thaw commences,
the water flows through the cracks in the pipes.

The greater number of solids must be liquefied before they pass
into the state of vapour. Nevertheless, camphor, arsenic, and some
other substances diminish in weight when exposed to the air, without
becoming liquid. Snow and ice do the same. Every one can observe

448 PHYSICAL PHENOMENA. [BOOK iv.

this fact during dry weather and hard frosts : pieces of ice and heaps
of snow perceptibly diminish in volume, or quite disappear, without
even partial fusion having taken place.

As regards liquids, they pass spontaneously for the most part
into vapour, at varying temperatures. Water 011 being placed in an
open vessel gradually disappears ; wet things dry with much greater
rapidity when the temperature is high and the surrounding air not
humid ; and again, when placed in a current of air, the water with
which they are saturated is converted still more quickly into vapour.
Mercury evaporates at ordinary temperatures ; a fact which was
placed beyond doubt by Faraday, by means of the following experi-
ment : he suspended a piece of gold leaf in a flask containing
mercury, and after some length of time he found that the leaf was
whitened. The mercury had thus amalgamated itself with the gold,
which could not have resulted unless evaporation had taken place.
This first mode by which liquids pass into the state of gas is called
evaporation. It is characterized by the fact that it is effected at
any temperature whatever, and solely at the superficial stratum of
the liquid. Vaporization, on the other hand, is the conversion into
vapour under the influence of a rise of temperature at the moment
when this temperature attains a fixed limit, determinate for each
liquid, and constant for the same external pressure. The liquid is
then in ebullition, that is to say, its mass is agitated by the passage
of the bubbles of vapour which have escaped from the bottom of
the vessel which contains it, and the specific lightness of which
causes them to ascend to the surface.

The temperature at which a liquid enters into ebullition is, as
we have just said, constant for the same pressure : that is, if the
liquid is always contained in a vessel of the same substance. Water
boils at 100°, at the barometric pressure of 760 millimetres, in a
metallic vessel ; in a glass vessel, however, it scarcely boils at 101°,
as proved by Gay-Lussac : this probably proceeds from a stronger
adhesion of the liquid molecules to the glass than to the metal.
Moreover, the temperature of ebullition remains constant during the
whole time that the vaporization of a liquid mass continues ; only
if a more intense heat is used, the passage into the vaporous state
is effected more rapidly.

The following are the temperatures at which vaporization (which

CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE.

449

v.--

always accompanies ebullition) takes place in the case of several
liquids : —

Ether 35°

Alcohol. ........ 80°

Water . 100°

Concentrated sulphuric acid . 325°

Mercury 350°

Sulphur 400°

Let us now study more closely the curious phenomena of the
ebullition or boiling of liquids, taking for our example that liquid
which is most easy to observe, viz. water.

When the temperature of a vessel containing water is raised by
placing it on the fire, the bottom and sides
of the vessel receive the first influence of >- :L xV~\

the heat. The heat is then communicated
to the contained liquid, which is at first
evaporated at the surface, this evaporation
being greater as the temperature of the
water approaches nearer to ebullition. At
length the moment arrives when vapour
is produced on the inner surfaces and at
the bottom of the vessel. The bubbles
there formed have an elastic or expansive
force, which, added to their specific light-
ness, causes them to rise to the surface of
the liquid. But the weight of the strata of
water and the atmospheric pressure are
opposed to this ascent, which does not
effectively take place until the elastic
force of the vapour is equal to the
sum of these two pressures. Then a tumultuous movement com-
mences, which is due to the passage of bubbles which burst at
the surface of the liquid. A little before ebullition, a peculiar
noise is heard : it is then said that the water sings. The pro-
duction of this noise may be explained as follows: when the first
bubbles of vapour rise to the surface, they traverse strata more
or less warm, the vapour of which they are formed is cooled and
condensed, and the surrounding water immediately fills the spaces

FIG. 297.— Ebullition In open air.

450

PHYSICAL PHENOMENA.

[BOOK iv.

which result. But the upper strata of the water soon attain the
temperature of the strata at the bottom, and the noise ceases, because
the cause of the condensation of the bubbles has disappeared.

The appearance of the bubbles of vapour confirms this explana-
tion ; they at first rise under the form of cones which taper off at the
upper part; when ebullition is complete they rise, on the contrary,
as cones widened at the top, because, instead of being condensed*
they are expanded in proportion as they overcome the diminishing
pressure of the liquid above them.

Experiment proves that, during the whole time of boiling of a
liquid, the elastic tension of the vapour which is formed is precisely
equal to the external pressure ; and because, as we shall presently
see, this tension increases with the temperature, it follows that the
temperature of ebullition of a liquid is lowered as the external pres-
sure decreases, and, 'on the contrary, that it is raised as the external
pressure increases. Thus, under a pressure of 760 mm. water boils
at 100°. De Saussure, having boiled water on Mont Blanc, found 86°

to bo the temperature of
ebullition, the barometric
pressure being 434 mm. ;
Bravais and Martins made
similar experiments, and
found the temperature of
ebullition at the Grands-
Mulets, on the sides of the
samemountain, 90°, under
a pressure of 529 mm., and
at the top of Mont Blanc
84 '4°, with a pressure of
424 mm.

In an apparatus called
(after its inventor) Papin's
Digester, the temperature
of ebullition of water is
raised at will, by increas-
ing the pressure on the surface of the liquid. The increased pressure
is produced by the vapour, which accumulates in large quantity
above the surface, and raises the boiling-point of the liquid. Papin's

FIG. 298.— Papin's Digester.

CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE.

451

Digester is composed of a cylindrical vessel made of iron or bronze,
with thick and excessively strong sides ; it is closed by a cover of
the same metal, which a pressure-screw presses against the edges of
the opening (Fig. 298). A hole in the cover allows the vapour to
escape whenever its tension exceeds a certain limit, which can be
fixed at pleasure by the following means: the hole in the cover is
closed by the arm of a lever, at the extremity of which is a weight
acting with a force proportional to its mass and the length of the
arm of the lever.

The limit of the elastic force of this vapour, or, in other words,
that of the temperature of the water contained in the vessel, can thus
be regulated beforehand. Water can be boiled at a constant tem-
perature far exceeding 100°, a temperature capable indeed of melting
tin, bismuth, and lead. Papin's Digester is used to dissolve or boil
in water substances which
require a higher temperature
than that of ebullition in free
air, at the ordinary pressure
of the atmosphere.

We have mentioned that
the ebullition of liquids takes
place at temperatures which
are lower as the pressure
decreases ; now, on placing
under the receiver of an air-
pump a vessel containing
water at a temperature below
100°, this liquid is seen to
enter into ebullition as soon
as, on rarefying the air, the
pressure falls to that of the
elastic force of steam at this
temperature ; the vapour thus formed accumulates above the surface
of the liquid, and by its increasing pressure ultimately stops the
ebullition. If the receiver is now cooled by means of a wet cloth,
the fall of temperature condenses a part of the vapour, and thus
diminishes the pressure, and ebullition recommences.

This experiment can be tried without the aid of an air-pump.

FIG. 299, — Ebullition of water at a temperature
lower than 100°.

452

PHYSICAL PHENOMENA.

[BOOK iv.

Water, contained in a bulb with a long neck, is submitted to a
lengthened ebullition, in order that the air may be completely ex-
pelled by the vapour which is formed ; the flask is then corked and
removed from the fire, and in order to prevent the entrance of air, the
neck is immersed in water (Fig. 299). The vapour which remains
above the liquid has a tension sufficient to prevent ebullition; but
if the bulb is cooled by pouring cold water over it, or by putting it

in contact with ice, the vapour is
condensed and ebullition recom-
mences : it seems as if water is boiled
by being cooled.

To understand thoroughly the con-
ditions under which the last change
of state — the liquefaction of gases —
which remains to be studied takes
place, it is indispensable for us to
know the laws which regulate the
formation of vapours in vacuo, the
experimental demonstration of which
is due to the physicist Dalton. The
following is an account of them : —
If we introduce into the Torri-
cellian vacuum a certain volume of
any liquid, for instance, a cubic centi-
metre of alcohol, the level of the
mercury is seen to be depressed, and
to stop at a point I (Fig. 300) ; and
its distance from the level of a
barometer, immersed in the same
basin as the first tube, measures the
tension or elastic force of the vapour
formed. We see at once that in
vacuo liquids pass spontaneously
into vapour.

Let us suppose that a thin stra-
tum of liquid is floating on the

mercury : if the tube is now raised without lifting the lower end
out of the mercury, the level will be observed to remain at I, that is

FIG. 300. — Spontaneous evaporation of a
liquid in the barometric vacuum. First
law of Dalton.

CHAP, ni.] EFFECTS OF VARIATIONS OF TEMPERATURE.

453

to say, at the same height as before. But the liquid stratum of
alcohol diminishes in thickness in proportion as the space occupied
by the vapour increases ; a fresh quantity of vapour is formed with-
out a change of tension ; and thus it continues until the whole of the
liquid is evaporated. If we now continue to raise the tube, that is,
to increase the space which the vapour occupies, the level of the
mercury will rise, which proves that the tension of the vapour
diminishes. The tube being
again lowered, the level falls
and comes back to the
point I; but if then the
same movement be con-
tinued, the level remains
constant, while an increas-
ing portion of the vapour
resumes the liquid form.
Figure 301 represents three
barometric tubes, the cham-
bers of which are filled with
the vapour of the same
liquid; as long as this re-
mains in contact with the
liquid itself, its tension does
not vary, which is proved
by the equal height of the
mercury in the three experi-
mental tubes.

From this first experi-
ment Dalton concluded :

1st. That a liquid placed in a vacuum vaporizes spontaneously.

2nd. That the vapour thus formed attains a maximum degree of
tension which remains invariable whilst an excess of liquid remains
in contact with the space filled with vapour. It is then said that the
space is saturated with vapour.

If we make the experiment with liquids of various kinds — water
alcohol, ether, &c. — we find that the maximum tension varies with
different liquids at the same temperature ; this is proved by the
different levels of the mercury in the barometer tubes shown in

FIG. 301. — Invariability of the maximum tension of the
same vapour at the same temperature. Dalton's
second law.

454

PHYSICAL PHENOMENA.

[BOOK iv.

Figure 302. If the temperatures are caused to vary, these phenomena
are produced in the same order, but the maximum tension increases
rapidly. The following table gives the tensions of aqueous vapour in
a vacuum, at different temperatures, expressed either by the number

Fio. 302. — Inequalities of the maximum tensions of different vapours at the same temperature.

Dalton's third law.

of millimetres of mercury which it supports in a barometric tube, or
by the number of atmospheres of 760 millimetres.

Temperatures.

Tensions. Temperatures.

Tensions.

mm.

— 10°

2-1

+ 120°

atmospheres.

0°

4-6

+ 134°

+ 10°

9.2

+ 144°

+ 20°

17-4

+ 152°

+ 30°

31-5

+ 180°

+ 40°

.55-0

+ 212°

+ 50°

92-0

+ 252°

+ 100°

760-0

+ 266°

By this table it is seen that at the ordinary temperatures, between
10° and 30° for instance, the maximum tension of aqueous vapour in
vacuo does not exceed 3-2 millimetres. A pressure higher than* 32

CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE. 455

millimetres, at the temperature of 30°, will cause a part of the vapour
to return to the liquid state. Nevertheless, we see water spon-
taneously vaporized in the open air, under a much greater pressure,
the mean being 760 mm. This is an apparent anomaly, which proves
the tendency which gases possess to rise by virtue of the expansive
force which belongs to them ; the air truly presses on the surface of
the water, but as air is a porous body, its molecules having spaces
between them, the molecules of aqueous vapour fill these intervals,
and thus mix with the gas of which the atmosphere is formed.

The laws of the mixture of gases and vapours were studied by
Gay-Lussac, who demonstrated that, if a space full of gas is saturated
with the vapour of any liquid, the maximum tension of this vapour is
precisely that which it possesses in a vacuum at the same tempera-
ture. The more the temperature is raised, the more vapour will a
space, whether vacuous or filled with gas, require to. saturate it.
Thus in summer, in very warm weather, there is often more aqueous
vapour in the air than in winter, during a damp and cold season.
This fact astonishes many people, who consider that clouds and fogs
are formed of aqueous vapour; but this is a mistake, for aqueous
vapour is always perfectly invisible and transparent. The very
minute drops of which fogs and clouds are formed are water in
the state of liquid, not of vapour ; in other words, they are aqueous
vapour which the lowness of the temperature has condensed. There
are, it is true, substances whose vapours are visible — for example,
iodine ; but this results from the fact that this vapour is not colour-
less like that of water, for it is of a beautiful purple-violet. Again,
the vapour of chlorine is visible, on account of its greenish-yellow
colour, that of bromine for its brownish-red colour.

When a gas or vapour is contained in a closed space, its lique-
faction can be produced by two methods — viz. either by lowering its
temperature or diminishing its volume. But, in ordei that the liquid
may appear, it is necessary that the space be previously saturated ;
and it is also by this same means of cooling or compression that
the state of saturation is obtained. By vapour is understood the
condition of a substance which was before in a liquid state. There
is no difficulty in liquefying any vapour, if we place it under the
conditions of temperature and pressure which it possessed when it
existed in the liquid state.

456 PHYSICAL PHENOMENA. [BOOK TV.

The liquefaction of gases presented many difficulties which by
degrees have been overcome. Ammonia gas, chlorine, carbonic acid
gas, and protoxide of nitrogen have been liquefied — and even, with
the exception of chlorine, solidified — thanks to the use of vigorous
processes of compression and refrigeration. Five gases now alone
remain which have not been liquefied by any known means ; these
are, hydrogen, oxygen, nitrogen, carbonic oxide, and binoxide of
nitrogen — a temperature of 110° below zero, combined with a pressure
of from 30 to 50 atmospheres, has left them still in the gaseous
state : for this reason they are called permanent gases. But induction
authorizes us to believe that it would be possible to reduce them,
like other gases, to the liquid state by using more powerful means,
for in a recent research Dr. Andrews of Belfast has shown it to be
probable that the various states of matter are continuous, the liquid
state forming a link between the solid and gaseous states — a link
however at times suppressed when the solid passes at once into the
gaseous or vaporous form — and he holds that the gaseous and
liquid states are only distant stages of the same condition of matter,
and are capable of passing into one another by a process of con-
tinuous change.

CHAP, iv.] PROPAGATION OF HEAT. 457

CHAPTER IV.

PROPAGATION OF HEAT. — RADIANT HEAT/

Heat is transmitted in two different ways, by conduction and by radiation —
Examples of these two modes of propagation — Radiation of obscure heat in
vacua — Radiant heat is propagated in a straight line ; its velocity is the same
as that of light — Laws of the reflection of heat ; experiments with conjugate
mirrors — Apparent radiation of cold — Burning mirrors — Refraction of heat ;
burning glasses — Similarity of radiant heat and of light — Study of radiators,
reflectors, absorbing and diathermanous bodies — Thermo-electric pile ; experi-
ments of Leslie and Melloni.

WHILE describing the effects of heat on matter, effects which
modify its volume, or change its physical condition, we have
said nothing of the manner in which the passage of heat from the
heat-source to the heated body is effected. When two bodies are
in the presence of each other, either in contact or at some distance
apart, experiment proves that an interchange of heat takes place
between them, how little soever their temperatures may differ; so
that each of them becomes a source of heat to the other: but we
more frequently reserve the term heat-source for that one of the two
bodies which possesses the higher temperature. We shall now study
the different modes of transmission of heat when it passes from
a heat-source to a body which is more or less distant, or when it
is transmitted through various media.

Experiment has shown us two principal modes of propagation
of heat, and the following examples may be easily multiplied by
adding our own daily observations. When a cold iron bar is held
in the hand by one of its extremities, the other end being placed
in the fire, a certain time elapses before the heat of the fire, which
is gradually transmitted along the bar, is perceptible to the touch ;
the shorter the bar, the less time does the heat take to travel along

N N

458 PHYSICAL PHENOMENA. [BOOK iv.

it; moreover, the intensity of the heat thus propagated increases
from the moment of the first impression, if the bar still remains
in the fire. Here, the heat has travelled along the metal, and from
molecule to molecule ; it is by the intervention of material particles
that it has thus been conducted from one extremity to the other
of the iron bar, and lastly communicated to the hand by contact.
This is an example of the propagation of heat by conduction. It is
in this way that the temperature of the exterior walls of a vessel
is raised, when hot water has been poured into the interior. The
same mode of transmission does not obtain, however, when the
heat of the fire is communicated to the face of a person who removes
a fire-screen quickly from before him, and thus becomes exposed
to its influence. In this case the rapidity of the impression proves
that it is not by warm air interposed between the fire and the face
that the heat of the fire has been propagated, but by a movement
analogous to that of light emanating from a luminous source. The
heat is then said to be propagated by radiation, and radiant heat
is that which is emitted from a source of heat and thus transmitted
to a distance.

Thus, when a source of heat is in the presence of, and at a cer-
tain distance from, a body, it can raise its temperature in two ways :
either by gradually warming, molecule by molecule, all the material
parts which are interposed between the body and the source, or
by warming the body directly, without an elevation of temperature
of the intermediate parts being a necessary condition to the elevation
of the temperature of the body. Heat is propagated by conduction
in the first instance, by radiation in the second.

As all other methods of transmission of heat may be included
in one or other of these, or by their combination, we shall study
them separately, and we shall commence with radiant heat.

Tbe action of the solar rays, which make themselves felt at a
distance of 91 millions of miles, proves that heat does not require
a medium of a ponderable nature for its propagation ; and, indeed,
when, after having traversed the interplanetary spaces, it enters the
atmosphere, and ultimately reaches the earth, it warms this latter
directly, without having raised to a perceptible degree the temperature
of the upper strata of the atmosphere, to which the cold which exists
in high regions of the air, on the summits of lofty mountains, testifies.

CHAP. IV.]

PROPAGATION OF HEAT.

459

Heat radiates from all the incandescent bodies which may be
observed on the face of the earth, in the same way as it emanates
from the sun. Obscure heat also possesses the same property, that
is to say, it is propagated from its source to any distance by direct
radiation, without warming the intermediate space, as during con-
duction. Eumford's experiment has placed this result beyond
doubt. He constructed a barometer, the tube of which was ter-
minated at its upper extremity by a large bulb, in the centre of
which a thermometer was placed ; the bulb thus formed the vacuous
chamber of the instrument, so that it was entirely void of ponderable
matter (Fig. 303). Having then closed the orifice of the stem,
and sealed off the bulb from it, he plunged the lower
part of this latter into boiling water; the mercury
in the thermometer rose immediately — an effect which
could be attributed only to the radiation across the
vacuum of the heat communicated by the water to
the mercury in the bulb.

Thus obscure heat radiates from calorific sources
in the same manner as luminous heat.

We will now show a more complete analogy be-
tween the phenomena of radiant heat and light ; the
same laws regulate both, so that luminous and calorific
effects appear to be produced by movements of the
same nature, for we are already aware of the existence
of heat-rays beyond the red end of the solar spectrum

Like light, radiant heat is transmitted in straight
lines through homogeneous media; if therefore we
interpose, between a source of heat and one of the

,,, /« -r T i T/V» • i ji • Fl°- 303.— Radiation

bulbs of Leslies differential thermometer, a series of obscure heat i»

VdC'UO,

of screens, each pierced with a hole, the instrument
will mark the elevation of temperature only so long as the holes of
the screens remain in a straight line. This experiment proves that
bodies exist of such a nature that radiant heat does not pass through
them : they are called adiathermanous substances. Other substances
which are traversed with more or less facility by heat- rays are called
diathermanous : these latter are generally transparent substances, such
as air and other gases; but there are also opaque bodies which
permit the passage of radiant heat, and are hence diathermanous.

N N 2

460

PHYSICAL PHENOMENA.

[BOOK iv.

The velocity of propagation of radiant heat is as great as the
velocity of light. The first series of experiments proved that there
is no appreciable interval between the moment when a screen, inter-
posed between a source of heat and a very sensitive thermoscope,
is removed, and that in which the instrument marks the elevation
of temperature. Mariotte worked thus at a distance of more than
100 metres : Pictet at 23 metres. But these experiments only prove
that the velocity of radiant heat is great, without giving its measure ;
it has since been proved that there is a perceptible difference be-
tween the velocity of the dark heat-rays of the solar spectrum and
of light rays.

FIG. 304. — Reflection of heat; experiments with parabolic conjugate mirrors.

Radiant heat is reflected from the surface of bodies, like light,
and in accordance with the same laws. We can assure ourselves of
this identity, by showing that the effects of a radiating source are
analogous to the luminous effects of reflection. Thus, if we place two
parabolic mirrors opposite to each other, so that their axes coin-
cide (Fig. 304), a source of heat placed in one of the foci will
transmit, to the nearest mirror, rays which will be reflected parallel to
the common axis, and after falling on the second mirror will, after
this new reflection, be reunited in its focus. This is what ought to
take place if the laws of the reflection of heat are the same as those

CHAP, iv.] PROPAGATION OF HEAT. 461

of light ; and we find that such is the case. In one of the foci we
place an iron basket containing burning coals, and in the other
focus some gunpowder, tinder, gun-cotton, or any other inflammable
substance, — it takes fire instantly. This experiment will not succeed, if
the source of heat or the inflammable body be displaced, however little,
from their respective foci. An experiment of Sir H. Davy has proved
that the laws of the reflection of radiant heat are the same in vacua
as in air. Moreover obscure heat is propagated like heat which
radiates from incandescent sources, which may be demonstrated by
the experiment of the conjugate mirrors by means of a vessel filled
with boiling water. This vessel is placed in one of the foci and the
bulb of a thermometer in the other, which immediately indicates a
rise of temperature. The same thermometer placed away from the
focus manifests no perceptible change.

We will now speak of a curious experiment which would lead us
at first sight to believe that cold can be radiated as well as heat.
If a piece of ice is substituted for one of the sources of heat, of
which we have just spoken, and if it is placed exactly in the focus
of one of the mirrors, the thermometer in the other focus falls, as
if a reflection of cold had taken place. The fact in this case is, as
in the others, that there are two bodies of unequal temperature in
the presence of each other, both of which radiate heat. Each of
them suffers a loss of heat, which is partly compensated for by the
gain which follows from the radiation of the other. In the first
experiment, the thermometer received more than it lost, and there-
fore there was an increase of temperature and an elevation of the
mercurial level. In the ice experiment, the thermometer on the con-
trary loses more heat than it receives; its temperature diminishes,
and the mercury sinks.

The laws of radiant heat have been utilized in obtaining a heat
of very great intensity at the focus of a spherical concave mirror
exposed to the solar rays. With an apparatus of this kind, which is
then called a burning mirror (Fig. 305), and which possesses a large
diameter and considerable curvature, metals have been melted,
bricks and stones vitrified, &c. Buffon obtained this effect from
spherical mirrors, by placing 100 silvered plane mirrors in such a
manner that each, of them was a tangent to the same sphere ; each
mirror turned on a hinge, and he thus increased or diminished the

462

PHYSICAL PHENOMENA.

distance of the focus at will. By means of this mirror he melted lead
at a distance of 140 feet (45'5 m.), and silver at 100 feet (22'5 m.).

The rays of heat which fall on a body are not all reflected. They
are generally divided into two groups. The first group consists of
the rays which are reflected from the surface of the body according
as we have just stated, to the laws of reflection of light ; there are
also other rays which are diffused in every direction; but none of
these rays penetrate into the substance of the body. The second

group is formed of the rays
which are absorbed by this
substance, and produce in it
an elevation of temperature,
being propagated by conduction
throughout the whole mass: and,
lastly, rays which pass through
the body, and issue in the same
manner as light traverses and
issues from transparent media.
The proportion of these differ-
ent fractions of incident heat
rays varies according to the
nature of the body which re-
ceives them, the state of its
surface, &c. Hence the expres-
sions, reflecting, diffusive, absorb-
ing, and diathermanous powers,
to designate the properties which
correspond to these different
modes of radiation of heat by various bodies. We shall speak of
these hereafter. At present we will confine ourselves to the pheno-
mena of the transmission of radiant heat through diathermanous
media, and to the laws of its propagation, because we shall find
an analogy between heat and light in this respect.

Heat-rays, when they enter a diathermanous medium, undergo
the deviation which we have studied in light under the name of
refraction. If the calorific beam falls perpendicularly on the surface
of the medium, there is no deviation. But at another incidence the
ray is deviated, and approaches the normal at the point of incidence, in

Fio. 305.— Burning mirror.

CHAP. IV.]

PROPAGATION OF HEAT.

46$

passing from one medium to another of a greater density ; in a word,
the laws of refraction of heat have been demonstrated to be like
those of the refraction of light. This fact has been proved experi-
mentally by using convergent spherical lenses to concentrate the
calorific rays which accompany the luminous rays of the sun. At the
focus, where the light is most intense, the heat is also the greatest ;
and every one can verify the truth of this fact, by setting fire, by the
aid of a magnifying-glass, to even a slightly inflammable substance by
the rays of the sun — tinder, linen, wood, paper, &c. This refers, it is
true, to sources of luminous heat ; but Melloni has proved by using

FIG. 306.— Refraction of heat.

prisms and lenses of rock-salt — which substance absorbs a smaller
amount of heat than any other — that obscure heat is refracted in
the same manner as that proceeding from an incandescent source.

The refraction of heat has been used, like its reflection, to produce
a very intense heat by the concentration of the rays of the sun. The
name of burning glass is given to every kind of lens constructed for
this purpose, whatever the diathermic substance may be. The power
of a burning glass increases with its diameter, and with the shortness
of the radii of the spheres to which the surfaces of the lens belong.
Tschirnhausen, celebrated for the construction of burning mirrors of
great power, made burning glasses nearly a metre in diameter, with
which he succeeded in melting metals and vitrifying mineral

464

PHYSICAL PHENOMENA.

[BOOK iv.

substances. Buffon obtained the same results with an echelon lens, —
that is, a lens, one surface of which is plane, while the other is cut
into concentric rings. The curvature of each of these rings is
calculated so that all the solar rays falling on the surface con-
verge to the same point (Fig. 307). In an apparatus of this kind,
the thickness of the glass being less than in an ordinary lens of
the same aperture, less heat is absorbed, and the calorific effect at
the focus is consequently more intense.

Burning glasses have also been constructed with various liquids,
the lens being formed of two convex glasses, enclosing a cavity

which contains the liquid
employed. Of these we must
quote the burning glass con-
structed in the last century
by Bernieres and Trudaine ;
it was four feet (1/33 m.) in
diameter, and had a focal
length of eight feet : when
filled with turpentine and
exposed to the solar rays,
calorific effects of extra-
ordinary intensity were ob-
tained.

We have most of us heard
that sailors, during voyages
to the frozen regions of the
poles, have been able to use
lenses of ice to procure fire.
In England very interesting
experiments were made with
an ice lens of great diameter
(3 metres), which proved the possibility of igniting powder and
paper at the focus of this novel kind of burning glass.

From the foregoing remarks we see that radiant heat is propa-
gated according to the same laws as light; its velocity is of the
same kind and degree; its direction is rectilinear in homogeneous
media; it is reflected and refracted similarly. The analogy has
become still more striking since the discovery that heat undergoes

FIG. 307. — Echelon lens.

CHAP, iv.] PROPAGATION OF HEAT. 465

double refraction in bi-refractive media ; and lastly, that it is also
polarized by reflection, and by simple and double refraction. It
is probable, therefore, that the calorific radiations do not differ
essentially from luminous radiations, that doth are due to the same
cause, viz. to vibrations of the ether ; but, whilst the disturbance
produced by the motion of the luminous waves affects the organ
of sight alone, that which proceeds from heat-waves, instead of
giving us the sensation of light, produces the sensation of heat.
Calorific and luminous radiations have even been considered as
possessing no other difference, except a greater or less rapidity of
the vibratory movement which gives rise to them. Thus the longest
undulations or the least refrangible rays — these expressions are
equivalent — would constitute the heat-rays, the obscure radiations ;
then increasing from a certain limit of rapidity, the vibrations,
without ceasing to produce heat, would impress the retina in the
form of light.

The theoretical ideas which assign a common origin to phenomena
apparently so different, and which are so, indeed, to our senses, are
becoming more and more plausible. The old hypothesis, which made
heat, light, electricity, and magnetism so many real and distinct
agents having a separate existence, is almost abandoned. We shall
soon see, in regard to heat, other proofs in favour of the new theory,
which show that heat is transformed into motion, and motion into
heat; a transformation incapable of being explained by the hypo-
thesis that caloric is a substance.

All bodies, whatever may be their temperature, emit or radiate
heat. We have described the experiment which proves that this
emission takes place with obscure heat as well as with luminous
heat. If, then, two or more bodies are in the presence of each other,
they will mutually radiate one towards the other, and we know that
the heat, received thus by each of them, will be partly reflected or
diffused, partly transmitted through its substance, and partly ab-
sorbed. It is this last portion only of the heat which has fallen on
the surface of a body which, being transmitted from molecule to
molecule, that is by conduction, influences its temperature.

When bodies which are near together and confined in a small
space are of unequal temperatures, experiment shows that the hottest
gradually cool while the others become warmer. At the end of a

466

PHYSICAL PHENOMENA.

[ROOK iv.

certain time equilibrium of temperature is established, which proves
that the interchange of heat ceases, or rather that it results in an
exact compensation between the losses and gains undergone by each of
them : the quantities of absorbed and of radiated heat are then equal
to each other. This last hypothesis, which is generally admitted, is
expressed by saying that the absorbing power and the emissive or
radiating power of a body are equal to each other. Moreover, the
hypothesis has been verified by experiment as regards temperatures
not exceeding 300°. Of this more presently.

The temperature of a source of heat influences the rapidity with
which it is cooled by radiation. Generally speaking, the higher the

FIG. 308. — Measure of the emissive powers of bodies. Experiment with Leslie's cube.

temperature, the more considerable is the emission, other circum-
stances remaining the same. This result may be proved by enclosing
the source of heat in a vacuum or in a space filled with a gas,
provided that the temperature be higher than that of the walls of
the enclosure, the rapidity of the cooling being also greater as the
excess of temperature itself is greater.

Emissive power depends also on the nature of the surface by
which the radiation is effected. Leslie proved the inequality of the
emissive power of different bodies in the following manner : —

As sources of heat, he took hollow cubes, the lateral faces of
which were formed of the substances whose emissive powers he
desired to compare; he then filled them with boiling water, which

CHAP, iv.] PROPAGATION OF HEAT. 467

was kept at a temperature of 100° by the heat of a spirit-lamp.
Each face of the cube A (Fig. 308) was turned successively towards
a concave mirror M, at the focus a of which was placed one of the
bulbs of his differential thermometer. To limit the rays of heat which
fell on the mirror, Leslie placed two screens, B, c, pierced with wide
apertures in the common axis of the mirror and cube, as shown in
Tig. 308. The action of the radiated heat produced a difference of
level in the two limbs of the differential thermometer, which became
stationary at the end of a few seconds. Operating in the same
manner with the different faces of its cubes, Leslie proved that the
nature of the radiating surface has a considerable influence on the
emissive power; and, as it has been proved that the emissive powers
of two bodies are proportional to the excess of temperature of the
two bulbs of the apparatus, he could form a comparative table of
their values for one temperature of the heat-source.

Since Leslie's time, the radiating powers of a great number of
bodies have been measured with other apparatus, and his result,
that lamp-black and white lead are the two substances which possess
the greatest amount of radiating power, has been verified. If we
represent the emissive powers of these substances by 100, the
emissive powers of the following substances, at the temperati*re of
100°, are as follows :—

Lamp-black . . .
White lead. . . .
Paper

100
100

Steel
Platinum ....
Polished brass

17
17

Glass

Red copper ....

Indian ink ....
Gum-lac ....

85
72

Polished gold . . .
Polished silver . .

3
3

We thus see that the metals . possess the least emissive power.
It was once imagined that bodies of bright colours radiated heat to
a less extent than those of a dull and dark colour, but the foregoing
table disproves this ; for white lead radiates as much as lamp-black.
The degree of polish of the surface of a body, a metal for instance,
influences its radiating power : in the case of a beaten or laminated
plate, if it is roughened its radiating power is increased ; on the
contrary, it is diminished if the plate is of cast metal ; which leads
to the supposition that the emissive power is in the inverse ratio of
the density of the superficial strata.

468 PHYSICAL PHENOMENA. [BOOK iv.

The preceding results account for a fact, which is easily proved,
that polished metal vessels, especially silver ones, preserve the
heat of the liquids contained in them for a long time ; but if this
surface is unburnished, and especially if it be covered with lamp-
black, the radiation becomes very intense, and the cooling of the
liquid takes place rapidly.

From a consideration of the radiating power of different sub-
stances let us pass to their reflecting power. And in the first place
we may remark that, in the case of a body which is not transparent
to heat or which is adiathermanous, of 100 heat-rays falling on its
surface, perhaps 20 will be absorbed; while all the others, to the
number of 80, will be reflected. Now, as the absorbing power is
itself equal to the emissive power, by a very simple calculation the
reflecting powers of bodies can be found without having recourse to
experiments. At the same time we must not forget that experiment
has led to the preceding reasoning ; and in physics, it is always more
instructive to learn anything experimentally, both as regards the
explanation of facts and the verification of laws.

Leslie compared the reflecting power of different substances, by
modifying the apparatus which he used for the study of their radiating
powers ; but we prefer the apparatus used by Melloni, as many other
researches connected with heat can be made with it.
The following is a description of it : —

A series of bars of different metals, usually bismuth and anti-
mony, B, A, . . . are soldered together at their extremities, and they are

arranged in such a manner that
all the even junctures are on
one side, and all the odd ones
on the other, as in Fig. 309.
The two extreme bars of the
series, one bismuth and the other
antimony, are connected by a

A BA BA BA BA B t • Ai • -

Vio. 309.-Elements of the thermo-electric pile. metal Wire; thlS formS a thermO-

electric pile. Whenever there is

a difference of temperature between the even and the odd joints,
an electric current is produced, either in one direction or the other,
but always passing from the bismuth to the antimony, on the
side which is at the highest temperature. Generally a" certain

CHAP. IV.]

PROPAGATION OF HEAT.

469

number of similar elements are united in a bundle, to which the
form of a rectangular prism is given, so that both faces are visible,
one formed by the even number of joints, the other by the uneven.

Whenever one or other of the faces of the pile is heated by
calorific radiation, the current will be produced ; and we must now
consider how its existence can be proved. The two conducting wires
are wound round the frame of a galvanometer — the desciiption of
which will be found in Book VI., which is devoted to Electricity — and
the current acts on the magnetic needle, causing it to deviate either
in one direction or in the other, according to the direction of the

FIG. 310.— Thermo-electric pile for the study of the phenomena of heat.

current. The extent of the deviation can then be read on the dial
of the galvanometer, and this shows the intensity of the current,
and, afterwards, the difference of temperature of the two faces of
this pile. The thermo-electric pile thus constituted is an instrument
of great sensibility : if we touch one of the faces with the finger, or
blow a puff of warm air upon it, it is sufficient to cause the needle
of the galvanometer to be considerably deviated ; on touching the
same face with a cold body, deviation takes place in the contrary
direction. Melloni employed the thermo-electric pile for the measure-

470 PHYSICAL PHENOMENA. [BOOK iv.

ment of the reflecting powers of different bodies, in the following
manner : —

At A (Fig. 311) a Locatelli lamp, which is a heat-source of
constant intensity, was placed ; B and c are two screens, one entirely
opaque, the other having an aperture or diaphragm, thus allowing
heat-rays from the lamp to pass through it, when the screen B is
removed.

On the stand D, a plate of the reflecting substance to be examined
is placed, and at E is the thermo-electric pile, moving on a scale H H',
which can be moved round the point H, so that the face of the pile
can be placed in the direction of the reflected calorific rays. Before
placing the plate on its stand, the scale is turned round the point

FIG. 311. — Apparatus used by Melloni to measure the reflecting powers of bodies.

H, and placed in a line with a scale which supports the pieces
A, B, c. The screen B is then lowered, and the deviation of the needle
of the galvanometer is measured, which gives the intensity of a ray
of heat radiated directly from the lamp to the pile, at a distance
equal to the total lengths of the scales. When the first measure-
ment has been effected, a second is made in order to give the intensity
of the reflected ray, and for this purpose the different parts of the
apparatus are placed as shown in the figure, the reflecting plate
being on its support, and the pile protected from direct radiation
by means of a large screen. On lowering the screen B, the rays
emanating from the source fall on the plate, are there reflected, and
strike against the face of the pile, after having traversed the same

CIIAP. iv.] PROPAGATION OF HEAT. 471

distance as the direct rays did in the first experiment. The needle of
the galvanometer is deviated to a certain extent, and the relationship
of the two deviations gives the reflecting power of the substance.

MM. La Provostaye and Desains have continued Melloni's re-
searches, and experimented on a great number of substances ; they
have measured their reflecting powers under different incidences,
varying the natures of the source of heat. They have discovered that
with any one body the reflecting power remains nearly constant, from
the normal incidence to an incidence of 30°; but afterwards it
increases rapidly, in proportion as the angle of incidence increases.
The reflecting powers of metals remain nearly constant for each of
them, in whatever manner their surfaces have been worked, pro-
vided that the degree of polish is the same. If the intensity of
the incident ray of heat be represented by 100, that of the reflected
ray is given by the following numbers, which refer to an incidence
of 50° :—

Reflecting powers. Radiating powers.

Polished silver ... 97 ..... 3

Gold ....... 95 3

Red copper 93 7

Polished brass .... 93 7

Platinum 83 17

Steel 83 17

Glass 10 90

Lamp-black .... 0 100

By comparing these numbers with those which measure the
radiating or emissive powers of the same substances, shown in the
second column, we find a proof of what has been before stated,
viz. that the radiating and absorbing powers of a body must be
equal; for the radiating, like the absorbing, power is the com-
plement of the reflecting power, at least for bodies which are not
transparent to radiant heat, and if we make due allowance for the
diffused heat.

Polished metals possess the greatest amount of reflecting power ;
when their surfaces are unburnished or rough, the heat-rays are
reflected in every direction, and the proportion of heat reflected
in a regular manner diminishes considerably as the proportion of
diffused heat increases. This phenomenon is analogous to that
observed under the same conditions in the case of light.

472 PHYSICAL PHENOMENA. [BOOK iv.

Leslie and Melloni also compared, by means of the two appa-
ratus before described, the absorbing powers of bodies ; that is to say,
the proportion of heat emitted from a constant source which enters
them and raises their temperature. They found that, in this respect,
the order of classification of the various substances is the same
as if they had been arranged according to their emissive powers ;
a result which confirms, to a certain extent, the equality of these
two powers proved by the reasoning adopted in the case of equili-
brium of temperature. We owe to Leslie the experimental determi-
nation of the fact that good reflectors of heat are bad radiators.

What has been aptly termed the Theory of Exchanges of radiant
heat, — a branch of the subject which has been investigated by Prevost,
Provostaye, Desains, Balfour Stewart, and Kirchhoff, — may be stated
as follows : —

I. If an enclosure be kept at a uniform temperature, any sub-
stance in it will at last attain that temperature.
II. All bodies are constantly giving out radiant heat indepen-
dently of the temperature of the bodies which surround
them.

III. Therefore, when a body is kept at a uniform temperature,
it receives back as much heat as it gives out, i.e. its
absorption is equ,al to its radiation.

This theory not only applies to the quantity of heat, but to its quality.
That is, it holds good not only in the case of dark rays, but of par-
ticular rays located in a particular part of the spectrum of a body
visibly luminous, as the spectrum of the light emitted by such a
body is built up of both heat-rays and light-rays, as we have seen.

Hence to these statements we must now add, according to the
researches of Balfour Stewart and Kirchhoff: —

IV. Bodies when cold absorb the same rays which they give

out when hot.

It will be seen that this is the same statement which we have
already made concerning light; it is in fact the basis of spectrum
analysis.

The influence of colour on the absorption of heat-rays has
been shown by Franklin's experiments. This illustrious physicist

CHAP, iv.] PROPAGATION OF HEAT. 473

placed pieces of differently coloured stuffs on the snow, and left them
for some time exposed to solar heat ; they absorbed the heat-rays,
became warm, melted the snow beneath them, and thus sank to
various depths, and deeper in proportion as the colour was darker.
From this result it was thought that bodies of light colour are bad
absorbers, and this again justified the supposed identity of rays of
light and rays of heat. But Tyndall has recently proved that this
conclusion is not quite exact. According to this physicist, the nature
of the source of heat must be taken into account ; obscure heat-rays
are not affected in the same way as luminous heat-rays. The
diathermanous power of substances must also be considered. Thus,
having taken two cards, one covered with white powdered alum
and the other with black powdered iodine, and having exposed both
to the fire, he found that the iodized card scarcely warmed at all,
while the card covered with alum became extremely warm ; he
explains this difference by the diathermanous property which
iodine possesses to such a high degree ; the radiant heat penetrates
the powder and is reflected on the limiting surface of the molecules,
without being absorbed by them. Moreover, a piece of amorphous,
and almost black, phosphorus, placed at the focus of the electric
light, cannot be ignited, whilst the same arrangement nearly instan-
taneously raises platinum to a white heat. Tyndall attributed this
curious effect to the diathermancy of the phosphorus.

This last property, possessed by certain substances, in virtue of
which they can be traversed by heat-rays without absorbing them, in
other words without their temperature being raised, exists in the most
marked manner in rock-salt. Of 1,000 rays which reach the surface
of a plate of this substance, 923 are transmitted; the 77 rays which
do not pass are reflected from the two faces of the plate ; consequently,
there is no absorption. This remarkable result, discovered by Mel-
loni, remains the same, whatever may be the nature of the heat-rays,
whether luminous or obscure.

Alum and glass are only diathermanous as regards the radiations
of luminous heat ; they arrest rays of obscure heat : this is also the
case with Iceland spar, rock-crystal, and ice. The thickness of
the plates has an influence on the absorption as on the trans-
mission of heat-rays; but this influence does not increase in pro-
portion to the thickness. Thus of 100 rays which reach two

o o

474

PHYSICAL PHENOMENA.

[BOOK iv.

diathermanous surfaces, one 'having double the thickness of the
other, 62 rays pass through the thinner, and 58 through the
other; a plate quadruple the thickness of the first allows 55 rays
to pass.

FIG. 312 — Mclloni's apparatus for measuring the diathermanous power of bodies.

The comparison of the diathermanous powers of different sub-
stances is made by means of Melloni's apparatus, arranged as in
Tig. 312. A plate of the substance the diathermanous power of

FIG. 313.— Cube of
boiling water.

FIG. 314.— Plate of blackened
copper heated to 400°.

Fio 315. — Incandescent
spiral of platinum.

which is to be measured, is supported on a stand D. The thermo-
electric pile is placed at E, in the direction of the rays of heat which
traverse the aperture made in the screen c. The deviation of the

CHAP, iv.] PROPAGATION OF HEAT. 475

needle of the galvanometer, produced by the direct rays without the
interposition of the plate, is first ascertained ; the plate is then placed
on its stand, and the deviation produced by the same rays traversing
the plate is noted. The relation of these two deviations gives the
diathermanous power of the substance.

To study the influence of the nature of the heat-source, Melloni
substituted in place of Locatelli's lamp a cube of boiling water,
a plate of blackened copper, or an incandescent spiral of platinum.
These different heat-sources are represented in Figs. 313, 314,
and 315. In the experiments he made on this subject, Melloni took
care, in order to compare the results, to place these different sources
at such distances from the pile, that the direct rays of heat produced
the same deviations on the needle of the galvanometer.

The following table shows the influence of the nature of the
source of heat on the transmission or on the diathermanous power of
different substances : —

Locatelli's
lamp.

Cube of water Copper Incandescent
at 100°. at 400°. platinum.

Direct radiation . . .
Eock-salt . .

100 ,
92
39
39
37 .
9 ',
6

, . 100 ,

, . 92 ,

, . 28 .
. . 24 .
. 28 ,
2 .
0

> .100 . .
, . 92 ..
6 . .
6 . .
6 . .
0 . .
0

100
92
0
0
0
0
0

Iceland spar ....
Glass

Rock-crystal ....
Aliun.

Ice ,

From these experiments we conclude that, as there are different
rays of light, so also there are different rays of heat which bodies
absorb and transmit in different proportions, nearly in the same way
as transparent bodies absorb some colours and allow others to pass.
Speaking of this property, Melloni used the word thermochroism,
derived from two words, the first signifying heat and the second
colour.

In terminating the foregoing remarks concerning radiant heat,
we may enunciate the following law relating to the decrease of in-
tensity with an increase of distance. As with light, the intensity
of radiant heat varies inversely as the square of the distance. A
very simple experiment, which we have borrowed from Tyndall's
work on Heat, proves the truth of this law, which may be deduced
by calculation.

o o 2

476 PHYSICAL PHENOMENA. [BOOK iv.

One face of the thermo-electric pile is furnished with a cone
which limits the dimensions of the sheaf of heat-rays, and which,
covered on the inside with black paper, can only reflect the heat
which falls obliquely on its inner surface. For the source of radiant
heat, a tin vessel filled with boiling water is used, one face of which
is covered with lamp-black ; this surface we use to prove the law,
by radiation towards the pile. The pile furnished with its cone
is placed opposite the vessel, at a given distance s o (Fig. 316);
the needle of the galvanometer is deviated to a certain extent ; the
-pile is then removed to double the distance s' 0; the positio'n of
the needle of the galvanometer remains constant ; and this is the
case for any other distance. For each of these positions, the total

FIG. 316. — Intensity of radiant heat. Law of the squares of the distances.

effect of radiation is therefore the same ; but the parts of the
surface of the vessel which send out rays of heat into the cone
are greater and greater ; these are circles whose diameters A B, A' B,
increase in proportion to the distance of the pile from the vessel,
and whose surfaces from that time continue to increase as the
squares of these same distances. It is therefore necessary that the
intensity of radiation should diminish in the ratio of these same
squares, in order that the effect produced on the pile may remain
constant. In a word, the augmentation of the efficacious radiating
surface is exactly compensated for by the diminution of the intensity
with the distance ; it is thus that the law has been proved.

CHAP, v.] TRANSMISSION OF HEAT BY CONDUCTION. 477

CHAPTER V.

TRANSMISSION OF HEAT BY CONDUCTION.

WE have already seen that, if we hold a bar of iron, one end of
which is placed in the fire, in the hand, the heat of the fire
is communicated to the metal, and is transmitted from molecule
to molecule along the bar; after a short time the temperature rises
so high that it commences to burn our hand, and obliges us to remove
it from the bar. If, instead of being iron, the bar, still of the same
diameter and length, is of another metal, a similar effect would be
produced ; but we observe that the length of time which the heat
takes to travel along the bar, and to heat it at any given distance
from the end to the same, temperature, varies with the nature of the
bar. The following simple experiment will prove the difference
which we have pointed out : —

Let us take two bars of equal dimensions, one of copper, the
other of iron, and fix small balls of wood by means of wax at equal
distances from the extremities of each ; if we place the bars, end to
end, and heat the extremities in contact by means of a flame of a
spirit-lamp placed at the point of junction, we shall see the balls
fall one after the other, as the wax is melted by the heat which is
transmitted by means of conduction along each of the bars. But at
the end of a certain time, the number of balls which have fallen from
the copper bar will be found to be greater than the number of balls
which have fallen from the iron bar. Moreover, two balls situated at

478

PHYSICAL PHENOMENA.

[BOOK iv.

the same distance from the source of heat but on different bars, do
not fall at the same instant.

We will for the present leave the consideration of the rapidity
with which heat is transmitted along each bar, and study the first
effect, viz. the comparative distance at which a certain degree of
temperature (here it is that of the fusion of wax) can be most quickly

Fio. 317.— Unequal conductivities of copper and iron.

attained by the two metals. Copper, in which we have found this
distance to be first attained, is said to be a better conductor of heat
than iron.

pipf

FIG. 318. — Ingeiihouz' apparatus for measuring conducting powers.

Fig. 318 represents an apparatus invented by Ingenhouz and
modified by Gay-Lussac, which is used to compare the conducting
powers of solids. Cylindrical rods of each of the substances to be
compared are covered with layers of wax of equal thickness, and are
placed horizontally, so that one of their extremities is immersed in
a bath of oil or boiling water, while the other passes through the
sides of the vessel which contains the liquid. The heat of the liquid
is transmitted along each rod, and melts the wax at distances which
are greater as the conductivity of the substance increases. Other
processes have been devised for the measurement of the conducting
powers of solids; but the one we have just described is sufficient
to show how different bodies can be arranged in the order of their

CHAP, v.] TRANSMISSION OF HEAT BY CONDUCTION.

479

conductivity. The following is the order and degree of conductivity
of the principal metals : —

Silver 1,000

Copper-
Gold .
Brass .
Zinc .
Tin

776
532
236
190
145

Iron 119

Steel 116

Lead 85

Platinum 84

Palladium 63

Bismuth . 18

Of all solid bodies metals are the best conductors of heat, always
excepting bismuth. Stone, glass, and marble are much less so than
metals ; lastly, wood-charcoal prepared at a low temperature, that is to
say not calcined, and organic substances generally, pulpy fruits and
plants, and the tissues of animals and vegetables, are bad conductors.
The preceding numbers indicate the great difference in the conduc-
tivities of metals. This difference may be illustrated in a very simple
way, by plunging two spoons, one of German silver and the other of
pure silver, into the same vessel of hot water. After a little time
the free end of the silver spoon is found to be much hotter than that
of its neighbour ; and if pieces of phosphorus be placed on the ends
of the spoons, that on the silver will fuse and ignite in a very short
time, while the heat transmitted through the other spoon will never
reach an intensity sufficient to ignite the phosphorus.

This fact is accounted for by the difference between the con-
ducting power of the silver and that of the German silver ; for the
first is represented by 1,000, the second by 60. The following
experiment demonstrates that the conductibility of a substance
does not depend on the rapidity with which heat is transmitted
through its interior. Two short cylinders of the same volume, one
of iron, the other of bismuth, have each one of their extremities
coated with white wax; they are then placed on the cover of
a vessel filled with hot water, their waxed ends being uppermost.
The heat of the vessel is transmitted through each cylinder, and
the wax on both will melt ; but that which covers the bismuth will
melt first. Nevertheless the conductivity of bismuth, according
to the foregoing table, is six times less than that of iron. What
therefore can be the reason of the phenomenon described? It is
due to the fact, that to raise the two metals of the same weight to

480

PHYSICAL PHENOMENA.

[BOOK iv.

Fig. 319. — Experiment on the conductivity of
iron compared with that of bismuth.

the same temperature, about four times more heat is required for iron
than for bismuth ; the heat received by the iron is therefore in great
part expended in raising its temperature, and this explains the

relative slowness with which the
transmission through its mass takes
place. To rightly observe the dif-
ference between the conducting
powers of iron and bismuth, it is
necessary to take two bars of the
same diameter, to measure the dis-
tances from the source of heat of
the points which possess the same
temperature at the moment of
equilibrium, and to take the squares
of the numbers which measure
these distances, which will give the
relative conducting powers.

The foregoing remarks refer to homogeneous bodies. In solids
whose structure is not the same in every direction — for example,
doubly refracting crystals, Iceland spar, quartz, &c. — the conductivity
varies with the direction of transmission of
the heat. There is a complete analogy be-
tween the mode in which heat is propagated
in these bodies, and that which relates to the
movement of light. Thus, let us take two
plates of quartz, one cut parallel and the
other perpendicular to the optic axis ; coat
both of the sections with wax, and pierce them
with a hole, through which a wire heated by FIG. 32o.-unequai conductivity

-i , • , . T . . , of quartz in difierent directions.

an electric current is passed: on passing the

current we observe that the wax melts around the wire ; but whilst
the stratum limiting the melted wax is an ellipse in the first plate,
in the second it is a perfect circle (Fig. 320), which proves the
unequal conductivity in the two directions. The conductivity of
wood is greatest in the direction of the fibres, and much less in a
direction perpendicular to this.

The unequal conductivity of different solids is utilized in many
ways. Tools and metal utensils, which require to be submitted to a

CHAP, v.] TRANSMISSION OF HEAT BY CONDUCTION. 481

high temperature, are furnished with non-conducting handles — of wood
or ivory, for instance — which almost entirely stop the transmission of
heat. Cotton, silk, and especially woollen fabrics, are bad conductors ;
they are therefore useful for preserving the body from excessive heat
or cold. In summer, they prevent the external heat from penetrating
to our bodies ; and in winter, on the contrary, the heat of the body
is retained on account of the difficulty of its transmission through
thick clothes. Moreover, it is not alone the substance of which they
are composed which gives this property to the fabric, for the mode
of manufacture also influences it. Between the threads, air is inter-
posed, which remains at rest, and, like all gases in a state of rest, it
conducts heat very badly ; heat therefore passes with great difficulty
through the fabric. Eider down preserves heat much better than a
closely made and heavier woollen coverlet would do.

We might multiply these examples to any extent, but will confine
ourselves to two or three curious experiments based on the differences
of conductivity of solids. A metal ball is tightly wrapped up in fine
cloth, in such a manner that the contact is close ; we then take a
coal from the fire and place it on the ball so enveloped. The fabric
will remain intact ; and if, to increase its combustion, the coal is blown
upon, the cloth will not be burnt. The reason of this is that the heat
received by the linen is immediately monopolized by the highly
conducting metal, and disseminated through its mass.

If before lighting a gas-lamp, a piece of fine wire-gauze is placed
above the jet, and the gas then turned on, it will spread below
and above the gauze. If it is lighted underneath, the combustion
remains confinecL to the lower part of the jet of gas; if, on the
contrary, it is lignted above, the upper part of the jet will alone
continue to burn (Fig. 321). In both instances, the interposition of
the wire-gauze is sufficient to limit the combustion, and the reason is
obvious : the meshes of the gauze form an excellent conductor of the
heat developed, which spreads rapidly over the wire, and does not
allow a sufficiently high temperature for the existence of flame on
the other side of the gauze. An important application of this pro-
perty of metallic gauzes exists in Davy's safety lamps, which are used
by miners. The metallic netting which envelops the light prevents
the ignition and explosion of the fire-damp — the dangerous gas which
escapes plentifully into coal-pits.

P P

492 PHYSICAL PHENOMENA. [BOOK rv.

Asbestos and amianthus are two silky mineral substances, noted
for their incombustibility. They are very bad conductors of heat, and
with a glove of amianthus a red-hot ball may be held in the hand
without danger. In this instance, the heat cannot be transmitted, it
is intercepted ; in the preceding example it is, on the contrary, rapidly
absorbed ; in both cases its transmission by means of conduction is
limited.

The experiments which have been made in order to measure the
conductivity of liquids and gases prove that it is very slight. Never-
theless, heat is transmitted with some rapidity through these media ;
it is, however, transmitted not by conduction but by convection, that is to
say, by direct transport of the heated parts. The cause of these move-
ments may be easily understood ; when a liquid is heated, its density

Fio. 321. — Property of metallic gauze ; obstacle which it opposes to the propagation of heat.

diminishes; then, as a consequence of the principle of Archimedes,
it tends to rise and to displace the denser strata above it. This
happens, when a liquid is heated at the bottom of the vessel which
contains it ; if the liquid is heated laterally, the "currents which are
established start only from the sides, instead of starting from all parts
of the bottom 'of the vessel ; the heating in this case is much less
rapid. The existence of currents is easily proved, if a material of
the same density as the liquid is mixed with it, such, for example,
as sawdust. This remains suspended in water, and on heating
the vessel the movement of the particles can be traced from top to
bottom and from bottom to top, proving the existence of currents :
the ascending currents proceed from the heated parts, which rise,
while the descending currents are due to the denser parts, which take
the place of the former. Heat is therefore diffused through the whole
liquid, and it is in this way that it is transmitted.

CHAP, v.] TRANSMISSION OF HEAT BY CONDUCTION. 483

Nevertheless, liquids possess some proper conductivity, as has
been proved by M. Despretz, who heated a liquid contained in a
cylindrical vessel from above. Twelve thermometers, the bulbs of
which were placed at different heights in the liquid, with their stems
outside, indicated decreasing temperatures from the upper strata
to the middle of the vessel, which was a metre in height ; the six
lower thermometers did not rise perceptibly. The conductivity of
liquids is thus established, but, as before stated, it is very slight.

The proper conductivity of gases has not been established ; all
that we know is, that they are certainly very bad conductors of heat.
Gaseous masses are heated like liquid masses, by transport or convec-
tion : in virtue of their great dilatability, as soon as a portion of a
gaseous mass is heated, either by radiation or contact, its volume
increases, and movements, which quickly heat the different strata,
result. The heat is thus conveyed as in liquids, but with still greater
rapidity. Again, if the movements of which we speak are confined
by enclosing the gas in the interstices existing between thin pieces of
fibrous substances, like cotton, wool, unspun silk, down, &c., the gas
acquires heat with difficulty, as has been proved by many experiments
of Thomson. Wo have already seen that it is partly owing to the
fact of gases being bad conductors of heat when at rest, that clothes
preserve the body from losing heat during cold weather.

484 PHYSICAL PHENOMENA. [BOOK TV.

CHAPTER VI.

CALORIMETRY. — SPECIFIC HEAT OF BODIES.

Definition of a unit of heat — Heat absorbed or disengaged by bodies during vari-
ations in their temperature — Specific heat of solids — Latent heat of fusion —
Ice-calorimeter — Latent heat of vaporization of water.

WHEN a body is heated or cooled through a certain number of
degrees, we say that it gains or loses a certain quantity of heat ;
but the thermometer which shows us these variations indicates nothing
as to the value of this quantity : we must not therefore give the pre-
cise etymological sense to the word thermometer. The thermometer
measures temperatures, not quantities of heat. We shall find, indeed,
that the heat necessary to raise a given weight of a body through a
certain number of degrees varies with the nature and physical condi-
tion of the body ; beyond certain limits of temperature, it varies also
for the same substance.

Before proceeding further we must explain what is meant by
quantity of heat. We know nothing of the intimate nature of heat ;
the analogies which we have endeavoured to establish between
radiant heat and light have induced physicists to imagine that
calorific phenomena, like luminous phenomena, are produced by
the vibrations of the ether ; but the manner in which these vibra-
tions, after penetrating into the interior of bodies, produce changes of
volume and condition is a question which science has not yet solved,
and which has only been answered by conjecture. Nevertheless,
researches of great importance have placed beyond doubt the im-
portant fact that heat can be produced by mechanical means, and,
conversely, that it can be transformed again into mechanical work
susceptible of being accurately measured ; in a word, that heat can

CHAP, vi.] CALORIMETRY. 485

be assimilated to force and measured like other physical forces.
We shall hereafter endeavour to explain what is understood by the
mechanical equivalent of heat.

Without passing beyond the domain of heat itself, we will now
state how it is possible to compare the quantities of heat which are
absorbed or disengaged during variations in the temperature as well
as in the changes of condition of solid, liquid, and gaseous bodies.
This division of the science of heat is known as calorimetry.

A unit of heat, or calorie, is the quantity of heat necessary to raise
from 0° to 1° centigrade one kilogramme (in England one pound) of
water. It is evident therefore that, if a certain number of calories
are requisite to raise the temperature of the unit of weight a
certain number of degrees, 2, 3, 4, .... more would be required to
raise the temperature the same number of degrees of a weight 2, 3, 4
times greater. Therefore the quantities of heat are proportional to
the weights. It is also considered as established, that the heat requi-
site to raise the temperature of a given weight through a certain
number of degrees, is equal to that which it disengages on returning
to its initial temperature. A very simple experiment also proves to
us that the quantity of heat absorbed during a certain elevation of
temperature is sensibly constant, whatever may be the initial
temperature.

Into a vessel which has been heated to 25°, a kilogramme of
water at 0° is poured, and a second at 50° ; then, after having rapidly
stirred the mixture, a thermometer on being plunged into it shows
the temperature of the mixture to be 25°. Thus the heat, transferred
by the kilogramme of water at 50° to the kilogramme at 0°, raises the
temperature of the second kilogramme to 25° ; at the same time, the
loss of heat undergone by the first has lowered its temperature from
50° to 25°. Finally, this experiment proves that the heat necessary
to raise a definite weight of water from 0° to 25°, would raise the
same weight of water from 25° to 50°. The initial temperature has
therefore no influence on the quantity of heat absorbed.

This, however, is only true within certain limits, which vary with
different substances : thus, two kilogrammes of mercury, one at 200°,
the other at 0°, mixed together, give two kilogrammes of mercury, not
at 100°, the mean temperature between the two extremes, but at
102°'85, a higher temperature than the mean. Beyond 100°, mercury

486 PHYSICAL PHENOMENA. [BOOK iv.

absorbs or disengages more heat for a like variation of temperature
than below 100°. Lastly, a third experiment shows that the quan-
tities of heat which we have just compared, vary with the nature of
the substances. If we mix separately one kilogramme of water at
0° with a similar weight of mercury or essence of turpentine at 100°,
or place in it a kilogramme of copper at 100°, a gain of heat for the
water and loss for the other substances will, as in the previous
instances, result ; and in each experiment it will be obvious that the
gain will be equal to the loss. But in the first instance the tempera-
ture of the mixture will be 3°'2, in the second 30°, and in the third
case 8°*6. We see therefore how much heat is requisite to produce
the same variation of temperature in equal weights of different sub-
stances. This is explained by saying that every substance has a
calorific capacity, or specific heat, belonging to it, and specific heat
may be defined as the quantity of heat which is necessary to raise
the temperature of a kilogramme (or pound) of a substance from
0° to 1°. This quantity of heat is expressed in calories or heat-
units, which evidently amounts to taking for unity the specific heat of
water.

Various methods have been employed by physicists for the
measurement of the specific heat of solids. One of these — the
method of mixtures — consists in plunging the body, the tempera-
ture of which is known, into a bath of water or any other liquid at
a determined temperature : when the temperature of the mixture has
become stationary, it is measured, and, by a simple calculation,1 the
relation of the specific heats of the solid and liquid is obtained. This
method is applied equally to liquids. Certain precautions are taken
when the bodies placed in contact exercise a chemical action on each
other ; moreover, the heat absorbed by the vessel is noted, that absorbed
by the thermometer itself is allowed for, and lastly the losses caused
by radiation are estimated. The following is a table giving the specific
heats of different solid, liquid, and gaseous bodies ; it proves that water

1 This calculation consists in solving an equation — the first part of which
expresses the quantity of heat lost by the body, and consequently transferred to
the bath and vessel : the second comprising two terms — the first, the heat gained
by the liquid ; the second, the heat gained by the vessel which contains it. It is
evident that, patting aside the external radiation of the liquid and vessel, the loss
and the gains are compensated ; hence the equation and solution of the problem.

CHAP, vi.] CALORIMETRY. 487

of all substances (with the exception of hydrogen, the specific heat of
which is three times that of water) absorbs or disengages the greatest
quantity of heat for equal variations of temperature : —

Substances. Specific heat.

Water 1*000

Hydrogen 3'294

Essence of turpentine 0*426

Air 0-207

Sulphur 0203

Glass 0-198

Iron 0-114

Copper 0-095

Silver ." . . . . 0'057

Tin 0-056

Mercury .;.-. :.-; ." . . 0'033

Gold 0-032

Platinum . . -, 0*032

Lead. . . ;:' '. ...'.. 0-031

Bismuth 0-031

But we must not forget that these numbers represent the quan-
tities of heat necessary to raise equal weights of these bodies from
0° to 1°, and that they only remain constant within certain limits
of temperature. They vary but little from 0° to 100°; but this is
no longer the case at higher temperatures. The specific heat of
mercury, for instance, which is 0*033 within these limits, becomes
0-035 beyond 100°. The physical condition of bodies also causes the
specific heat of the same substance to vary ; in the solid state it is less
than in the liquid state, and in the gaseous state it regains sensibly
the value which it had in the solid state : thus the capacity of ice,
which is nearly equal to that of steam, is scarcely half that of
water. When the density of a metal is increased, by hammering
for example, its specific heat is diminished. This explains, to a certain
extent, a result deduced from the preceding table, viz. that the densest
bodies have generally the smallest capacity for heat.

Dulong and Petit discovered a remarkable law, which has been
verified by M. Regnault in his beautiful researches on the specific
heats of bodies. It is well known that chemists consider simple
bodies as formed of irreducible parts or atoms, the weight of which
is called the chemical equivalent of the body. The weight of the
atom of hydrogen being taken as unity, that of an atom of mercury

488 PHYSICAL PHENOMENA. [BOOK iv.

is 100, that of sulphur 16, and so on. This being granted, let us
now inquire what quantity of heat will be necessary to raise the tem-
perature of an atom of sulphur 1° ; and what quantity likewise will
be absorbed by an atom of mercury to raise its temperature 1°. It is
evident from the foregoing, that we must multiply the weights 100
and 16 of each atom by the specific heat of the simple body to which
it belongs ; that is to say, by 0'033 and 0-203 : the products will be
proportional to the quantities of heat sought. Now, 100 x 0'033
gives 3'3, and 16 x 0'203 gives -3'248 : the products are thus sensibly
equal, and the same happens if we take any other two simple bodies.
This law may be enunciated as follows : — the same quantity of heat
is required to raise the temperature of an atom of any simple body
the same number of degrees ; or, again, the atomic specific heat is the
same for all substances.

We have seen that the specific heat of water is nearly four times
greater than that of air; thence it follows that 1,000 kilogrammes
of water, on being cooled 1°, disengage an amount of heat sufficient
to raise the temperature of 4,000 kilogrammes of air 1°. But
4,000 kilogrammes of air occupy, under the normal barometric
pressure and at 0°, a volume 770 times that ,of a like weight of
water; that is to say, a volume of 3,080 cubic -metres: the con-
sequences of which fact are thus explained by Tyndall in his work
on Heat: —

" The vast influence which the ocean must exert, as a moderator
of climate, here suggests itself. The heat of summer is stored up in
the ocean, and slowly given out during the winter ; hence one cause
of the absence of extremes in an island climate. The summer of the
island can never attain the fervid heat of the continental summer, nor
can the winter of the island be so severe as the continental winter.
In various parts of the Continent, fruits grow which our summers
cannot ripen ; but in these same parts our evergreens are unknown ;
they cannot live through the winter cold. Winter in Iceland is, as a
general rule, milder than in Lombardy."

In quoting these remarks, we must not forget that the particular
facts related by Tyndall do not depend only on the vicinity of the
ocean and the high specific heat of water, but also on the elevation
of temperature in Iceland by the great lukewarm current of water
known as the Gulf Stream.

CHAP, vi.] CALORIMETRY. 489

In describing the phenomena of the fusion of solids, and the vapori-
zation of liquids, we insisted on the general fact, that the temperatures
of the melting and of the boiling point are fixed for each body,
independently of the intensity of the source of heat which determines
the result, or the rapidity with which these changes of condition are
effected. These temperatures are the same, moreover, as those of the
inverse phenomena of solidification of liquids and liquefaction of
vapours. Thus, when a piece of ice melts, its temperature remains con-
stant at 0°, and all the heat furnished by the fire, whatever may be its
intensity, is consumed in reducing the ice to the liquid condition and
in maintaining this condition. We have here, therefore, a quantity
of heat absorbed by a body which does not raise its temperature, and
consequently does not become sensible to the thermometer. On this
account it is called latent heat. It is the latent heat of fusion or
liquidity, or, better, the latent heat of elasticity, according as it refers
to the passage from the solid to the liquid condition, or to the passage
from the liquid to the gaseous condition. It is very evident, therefore,
that the heat which is absorbed in these two instances is disengaged
when the substance returns to its primitive condition. The latent
heat of different substances has been determined by methods
analogous to those which are employed in the case of specific heat.
We shall confine ourselves here to the results obtained in the melting
of ice, because it will enable us to describe another process for
determining the specific heat of bodies.

It has been found that the latent heat of fusion of ice is 79'25
calories ; that is to say, that the quantity of heat absorbed by a kilo-
gramme of ice during melting, would be sufficient to raise 79*25
kilogrammes of water from 0° to the temperature of 1° ; or again,
to raise a kilogramme of water from 0° to 79°'25. Therefore, when
a kilogramme of ice at 0° is melted in a kilogramme of water at
790<25, the two kilogrammes of water produced possess a temperature
of 0°. The knowledge of this result permits the determination of the
specific heat of a body by ascertaining experimentally the weight of
the ice which can be melted by lowering its own temperatu-re to 0°.
The following is the process : —

A cavity is made in a compact and homogeneous block of ice, the
sides of which are carefully dried ; a piece of the substance whose
specific heat is sought, the temperature of which is above 0°, is then

490

PHYSICAL PHENOMENA.

[BOOK iv.

introduced ; a thick plate of ice is then placed over the cavity, to which
it serves as a covering (Fig. 322). During the act of cooling, the
substance melts a portion of the ice with which it is in contact, and
the resulting water is collected and weighed.
Let us suppose that the result is 100 grammes
of water, it is evident that the heat disengaged
by the body during its cooling to 0°, has been
the tenth part of 79'25 calories or *7'925 calories.
By hypothesis the body weighed 2 kilo-
0^^ and was at first at the temperature

350 . then dividing 7.925 by 35> and after.

calorimeter.

wards by 2, the quantity of heat disengaged by 1 kilogramme for a
variation of 1° will be found ; that is to say, the specific heat of the

FIG. 323.— Measure of tlie specific heat of bodies by the ice calorimeter of Laplace
and Lavoisier.

body. In the particular case we have chosen it would be 0113, the
specific heat of iron.

CHAP, vi.] CALORIMETRY. 491

Instead of ice cavities, the ice calorimeter invented by Laplace
and Lavoisier may be preferably employed. Fig. 323 represents it in
section and elevation. It is an instrument formed of three vessels,
which are placed one within the other, while the spaces between them
are filled with pounded ice. The heated body is placed in the smallest
vessel ; during cooling it melts a certain amount of ice, and the water
is collected by a stopcock at the bottom of the vessel. The ice
between the two outer vessels prevents the fusion, by external heat,
of that which is in contact with the heated body.

These methods do not give very exact results ; if we have preferred
them to more perfect methods, it is because our aim is principally to
explain the possibility of measuring quantities of heat. Those who
desire to extend their knowledge on this subject must have recourse
to special works, among which we may mention the beautiful Memoirs
of M. Eegnault on the specific heats of vapours and gases.

A kilogramme of water, at the boiling-point, or 100°, requires 536
calories in order to convert it into steam. During the condensation
of the steam thus formed, it will disengage the same quantity of heat ;
the application of steam to the warming of buildings is based on this
fact. In the arts, the latent heat of steam is also employed to raise
the temperature of large masses of liquid.

492 PHYSICAL PHENOMENA. [BOOK iv.

CHAPTER VII.

SOURCES OF HEAT.

IT follows from our foregoing study of calorific phenomena, that
two or more bodies when in the presence of each other make
a mutual and continuous exchange of heat, either by radiation at a
distance, or by conduction. From this point of view, a piece of ice at
0° C. is a source of heat to a body which is at a lower temperature
than its own.

However, in general language, this expression " source of heat," or
" heat-source," is more particularly reserved for bodies which possess
high temperatures, and which emit in a continuous manner a certain
quantity of heat for a limited or even for an apparently indefinite
time. Incandescent solids and gases, fire and flame, are sources of
heat according to this view: in the same category may be placed
bodies which emit obscure heat at a high temperature, for instance
boiling water.

Lastly, the expression " source of heat " is also given to the
different modes of production of heat: in this sense, friction, per-
cussion, electricity, and combustion — that is to say, certain physical
or chemical actions — are sources of heat. The heat which organized
and living bodies emit, is of the same order.

Sometimes sources of heat are classed as temporary and accidental,
natural and artificial, cosmical and terrestrial ; but these distinctions,

CHAP, vii.] SOURCES OF HEAT. 493

which are not based on the nature of the heat-sources, teach us
nothing more than that there may be a particular study of each
kind. We will therefore review them one after the other, beginning
with the sun, the most important of all, — at least to the earth.

The appearance presented to us by the sun is probably due
to an enormous layer of cloud built up of solid or liquid incan-
descent particles, the layer being surrounded by an absorbing
gaseous atmosphere; as is proved by the analysis of the solar
spectrum. The opinions of men of science are divided as to the
nature of the nucleus : some regard it as an incandescent solid or
liquid, others as a gaseous mass likewise incandescent. "We know
nothing of the way in which the immense amount of light and heat
is renewed and maintained : it radiates in every direction into
space, and its intensity does not appear to have sensibly varied
for thousands of years.

The intensity of the solar heat, as it reaches the surface of the
earth, has been calculated by Sir J. Herschel at the Cape of Good
Hope, and M. Pouillet in Paris. The instrument used by the latter
for this determination, which he called the pyrkeliometer, is repre-
sented in Fig. 324. At the upper part we notice a very thin
silver cylindrical vessel, the face of which is turned towards the sun
and is covered with lamp-black ; this vessel is filled with water, and
the temperature of the liquid is indicated by a thermometer whose
bulb is immersed in the interior of the cylinder, and whose tube is
protected by a brass tube pierced longitudinally with a groove so
that the level of the mercury can be seen. At the other end of the
tube is a disc of the same diameter as the cylindrical vessel, which
receives the shadow of the latter, and indicates whether the black-
ened surface is exposed normally to the direction of the sun's rays ;
this is the case when the lower disc is exactly covered by the circular
shadow of the upper one. The temperature of the instrument in
first noted ; its blackened face is then exposed to a portion of the
sky without clouds, but in such a manner that it does not receive the
solar rays : at the end of five minutes its radiation has produced a
certain lowering of temperature. The instrument is then directed
towards the sun ; the blackened face receives the solar heat falling
perpendicularly upon it for another five minutes. The elevation of
temperature is now noted, and the instrument is again caused to

494

PHYSICAL PHENOMENA.

[BOOK iv.

radiate its heat for five minutes in its first position ; the final cooling
must then be observed. The first and third observations are neces-
sary for the calculation of the quantity of heat lost by radiation by
the instrument during its exposure to the sun, — this quantity being
a mean between the two observed coolings. By adding to it the
heating due to direct exposure to the sun, the total elevation of
temperature will be obtained ; and consequently the number of
calories can be calculated which have been absorbed during a
minute by a surface equal to that of the blackened disc.

FIG. 324.— M. Pouillet's Pyrheliometer.

This quantity of heat depends, as a matter of course, on the eleva-
tion of the sun above the horizon ; for before reaching the surface of
the earth, the heat-rays of the sun traverse the atmospheric strata,
which absorb a certain proportion increasing with their thickness.
M. Pouillet has studied the law which regulates the calorific
intensity of the sun according as its height varies, and he has de-
termined the absorption due to the atmosphere if the sun were at

CHAP. VIL] SOURCES OF HEAT. 495

the zenith. This absorption varies to a certain extent according to
the purity of the atmosphere, and may rise to 0'25 ; that is to say,
to one-fourth the amount of heat which would reach the earth if the
atmosphere did not exist.

Considering the total heat received by an entire hemisphere, and
consequently at every possible degree of obliquity, it is found that the
proportion absorbed by the atmosphere is comprised between four and
five tenths of the heat emitted by the sun, if the sky were entirely
without clouds. The surface of the earth therefore scarcely receives
more than one-half of the solar heat, this being distributed unequally
according to the obliquity of the rays ; the other half warms the
atmosphere.

Supposing the heat received by the earth to be uniformly dis-
tributed, M. Pouillet has calculated that a square centimetre receives
O441 calorie per minute ; that is to say, a quantity of heat sufficient
to raise the temperature of 441 grammes of water 1°. In one year,
each square centimetre receives 231,675 calories : the quantity of
heat received in a year by the entire earth would be sufficient to melt
a layer of ice 100 feet in thickness surrounding the globe.

From the quantity of heat received annually by the earth, the
total amount of heat radiated by the sun into space can be deduced.
This may be done by calculating how many times the surface of a
great circle on the earth, i.e. an area equal to a section of the
earth, is contained in the surface of a sphere which has the centre
of the sun for its centre, and the distance from this body to our
globe for its radius. An easy calculation gives 2,150.000,000, so that
the heat intercepted by the earth is only ^ T^O.^OO-.TTOTT Par^ °f tne entire
solar radiation. " The heat emitted by the sun," says Tyndall, " if
used to melt a stratum of ice applied to the sun's surface, would
liquefy the ice at the rate of 2,400 feet an hour ; it would boil, per
hour, 700,000 millions of cubic miles of ice-cold water. Expressed
in another form, the heat given out by the sun per hour is equal to
that which would be generated by the combustion of a layer of solid
coal ten feet thick, entirely surrounding the sun ; hence the heat
emitted in a year is equal to that which would be produced by the
combustion of a layer of coal seventeen miles in thickness."

Such is the calorific intensity of the immense body which furnishes
the earth and the other planets with their supply of heat, and, as we

496 PHYSICAL PHENOMENA. [BOOK TV.

shall presently see, their provision of life and mechanical force. We
do not yet know how this prodigious activity is maintained ; never-
theless, several ingenious hypotheses have been made concerning it,
but these, we must remember, rest mainly on conjecture.

The earth also receives heat-rays emitted by the stars, which are
heat-sources similar to that of which we have just spoken. At the
almost infinite distance of the stars, the heat radiated by them is so
feeble as to be all but inappreciable : indeed, it is almost impossible
to measure it. Nevertheless some successful attempts have been
made by means of large telescopes which grasp a large number of
these radiations, and delicate thermo-electric piles. Thus Mr. Stone
has found that the heat received from Arcturus is equal to the
radiation of a Leslie cube of boiling water at a distance of 383
yards. The whole of these distant radiations, that of the sun
excepted, determines what is called the temperature of space, which
has been estimated by many savants. According to Fourier, this
temperature is — 60° C. ; M. Pouillet states that it is much lower,
and can scarcely exceed — 140° C.

The surface of the ea,rth also receives heat from its interior — heat
which belongs to the terrestrial globe itself, as Fourier has proved.
At a certain depth below the surface, a stratum is found with a
constant temperature which is nearly the mean temperature of
the place.

Below this stratum the temperature increases, and its mean
augmentation is about 1° for 100 feet. If this increase of heat,
which has been proved to a depth exceeding 2,400 feet, continues in
the lower strata and in the same proportion; at 2 miles the
temperature would already reach the boiling-point, and at 25 miles
most of the known minerals would have attained their melting
points. But it remains to be asked whether the enormous pressure
to which the terrestrial strata are subjected at this latter depth,
is not an obstacle to their liquefaction: the incandescence of the
terrestrial nucleus thus remains in an hypothetical state. There
are mechanical reasons, as Sir William Thomson has shown, for
believing that the whole earth must be as rigid at least as a solid
globe of glass, so that the theory of a fluid central core seems
incredible.

The sun is the most abundant and economic source of heat : but

CHAP. TIL] SOURCES OF HEAl 497

we cannot adapt it at will to our purposes, and, when it is clouded
over, or invisible, we most require heat : and unless it is concentrated
by expensive apparatus, it only produces comparatively low tem-
peratures. Civilization would be impossible if man had only the
solar heat at his command, and had not discovered artificial sources
of heat. Combustion, that is to say, the chemical combination of
certain bodies with oxygen, constitutes one principal source of this
kind, and the term artificial heat-sources is applied to those which
can be used at will, and the intensity of which can be regulated
according to the wants of the moment.

Generally speaking, whenever substances enter into combination,
heat is disengaged. Thus, a mixture of water and sulphuric acid, and
of water and a certain quantity of quicklime, is accompanied by a
considerable rise of temperature.

The combination of oxygen, one of the constituents of . our atmo
sphere, with certain solid or gaseous elements, gives rise to a very
intense disengagement of heat accompanied by light, and frequently
produces the phenomenon of vivid
combustion. But in order that a
combustible body may burn, either
in the air or in pure oxygen, one
of its parts must first be brought
to a high temperature ; in fact, it
must be lighted. When once the
combination has commenced, the
heat disengaged by it is communi-
cated in succession until the com-
bustible gas is entirely extin-
guished, or the body with which
it is combined is completely con-
sumed. It is thus that We Obtain FIG- 325.— Combustion of iron in oxygen.

fire in our stoves and the light of our candles and lamps ; and we
know by experience that these sources of heat and light only last so
long as they are kept up, — that is to say, while they are furnished
with the two elements necessary for the combustion.

When combustion takes place in pure oxygen, it is much brighter
than in air. On plunging a steel spiral furnished with a piece of
burning tinder into a bell-jar filled with this gas (Fig. 325), a very

Q Q

498 PHYSICAL PHENOMENA. [BOOK TV.

bright combustion of the metal is produced, and it sends out a
number of sparks in every direction.

The phenomenon of combustion is complex, but we can only say
here that the flame proper must be distinguished from the solid
incandescent portions. In order that a body may burn with a flame
there must be a disengagement of certain gases under the influence
of a high temperature; and these gases, becoming luminous, produce a
moveable light. In the flame of a candle or jet of gas there are three
distinct portions in which the heat and light are associated in
different proportions.

The exterior layer is the seat of the most active combustion and
of the highest temperature,1 but the light of this region is not intense ;
next comes a very luminous stratum where the
combustion is always less complete, and the heat
less intense, but which shows great brilliancy :
whether this is on account of the very fine
particles of incandescent carbon of which it con-
sists, or on account of the density of the vapours,
is not yet decided. Lastly, at the interior of the
flame, there is a dark space, at a much lower tem-
perature, because, as the oxygen of the air cannot
penetrate to it, the gaseous matters which fill it are
not burnt. It is only on reaching the top of the
flame that these matters are burnt in their turn :
when the combustion is incomplete, they rise in the
form of smoke.

If the flame of a candle is blown upon quickly,
we all know what happens, — the light is extin-
FIQ. 326.— Fiame of a guished ; and the reason is simple: by the act of
blowing, cold air is introduced into the inflammable
gas, which cools on being diffused into a quantity of cold air ; the
temperature then falls to such an extent that combustion ceases.
If, after having blown out the flame, the wick remains incan-
descent, by blowing it lightly it is again lighted, because the

1 A spectroscopic examination of a candle-flame affords a very beautiful proof
that the outer flame is the hottest, for this region gives us the bright line of
sodium, which would be a dark line, when the spectroscope is directed to the
brighter part of the flame, if the outer flame were not the hottest.

CHAP. VII.]

SOURCES OF HEAT.

499

oxygen necessary for the combustion is introduced, and the gas again
disengages itself, and is inflamed at the point of contact of the solid,
incandescent parts.

Several physicists — among others, Laplace, Lavoisier, Rum ford,
Despretz, Dulong, Fabre, and Silbermann1 — have endeavoured to
measure the quantities of heat which are disengaged during chemical
combinations, and especially during ordinary combustion. The
number of calories which are disengaged when a unit of weight of a
combustible body is burned, is what is called the heat of combustion
of that body. We cannot describe the methods which have been
employed in these important researches, and shall only give some
results which show to how great an extent the elements differ in
this respect. Whilst the heat of combustion of 1 gramme of native
sulphur is 2,260 calories (the calorie
is in this case the quantity of heat
necessary to raise 1 gramme of
water 1° C.), that of 1 gramme
of carbon in the state of dia-
mond is 7,770 calories; the same
body in the state of natural
graphite is 7,796 ; and lastly, as
charcoal, 8,080 calories. Hydrogen
burning in chlorine disengages
23,783 calories, and the same gas
burning in oxygen 34,462.

The heat of combustion of
hydrogen is the most intense of
all; it has been calculated that
it corresponds to an elevation of
temperature of 6,800° ; which has
led to the employment of this
extreme heat for the production of extremely high temperatures.
MM. H. Sainte-Claire-Deville and Debray, by using the oxy-
hydrogen blowpipe, have fused considerable masses of platinum ; a
kilogramme of this metal requires for its fusion, and for keeping it
in a state of fusion during the time of refining, a consumption of
70 litres of oxygen and 120 litres of hydrogen.

1 Andrews of Belfast has made very accurate experiments on this subject.

Q Q 2

Fio. 327.— Oxyhydrogen blowpipe.

500 PHYSICAL PHENOMENA. [BOOK iv.

Mechanical action, friction, percussion, and compression, develop
heat, just like the more intimate motions which constitute the phe-
nomena of chemical combinations. There are numberless examples
of this transformation of motion into heat, and we can each observe
them for himself. We will mention some of them.

When a metal button is quickly rubbed against cloth or any solid
body, it becomes warm, and finally very hot : schoolboys well under-
stand this experiment. The friction of a saw against the piece of
wood which it is dividing, that of a razor or knife which is being
ground, of a file against the metals which it wears away, raises the
temperature of the objects subjected to these violent motions, the
molecules of which are thus disturbed. The sparks produced by
horses' shoes on the pavement, or by the friction of the steel on the
wheel of a grindstone, or those which set light to tinder in the flint
and steel method, all proceed from the high temperature produced by
friction; very fine metallic particles are detached, and the heat
developed is sufficient to set the little masses on fire.1

Very dry pieces of wood rubbed against each other become
heated ; smoke is disengaged, and, if we may believe the stories of -
travellers, savages by these means procure fire. Turners sometimes
produce black bands on the objects which they are making by
pressing a piece of wood against the spot which they wish to char.
The heat which follows from this pressure, joined to the rapid rotatory
movement of the lathe, is strong enough to carbonize the wood on
the circumference of the object. The pivots of machines, the axle
of carriages and railway carriages, become strongly heated by the
friction which results from a rapid and prolonged rotation ; indeed
they would take fire, or get red-hot, if care were not taken to lubri-
cate or grease them.

We may quote here, as an example of the enormous quantity of
heat which can be disengaged by the friction of two solids against
each other, the celebrated experiment made by Eumford in 1798 ; this
experiment had been suggested to $iat celebrated physicist whilst he
was superintending the boring of some pieces of cannon at Munich.

1 " Before the discovery of Davy's safety -lamp, the fire-damp was the great
trouble of mines ; and many mines remained unexplored and inaccessible on account
of the presence of this invincible enemy. As common lamps could not be used,
the passages were illuminated by means of a steel wheel which was caused to turn
against a gun-flint." — SIMONIN, La Vie Souterraine

CHAP, vii.] SOURCES OF HEAT. 501

Struck by the great quantity of heat disengaged during this operation,
he wished to measure it as exactly as possible ; accordingly he placed
a metal cylinder, destined for the operation of boring, in a wooden case
filled with water, the temperature of which was shown by an immersed
thermometer. An hour after the friction of the blunt borer against
the cylinder had commenced, the temperature of the water, at first
16°, rose to 46°. At the end of two hoars, it was 81°, and again,
half-an-hour later, the water completely boiled. "It would be
difficult," said Eumford, " to describe the surprise and astonish-
ment expressed in the faces of the assistants at the sight of such
a quantity of water (about two gallons) heated and caused to boil
without any fire."

The friction of solids against liquids and gases also develops heat.
Joule's experiment, to which we shall presently refer, proved the
heating of a liquid when agitated by metallic paddles turning on an
axis. The incandescence of aerolites is due to friction against the
atmosphere, which they enter with considerable velocity. The eleva-
tion of temperature caused by the friction of a gas against a solid is
placed beyond doubt by a very simple experiment made by Tyndall
in his Lectures on Heat : by means of a pair of bellows he caused
a current of air to impinge on one of the faces of a thermo-electric
pile ; the needle of the galvanometer was immediately deviated, and
the direction of the deviation indicated that the face of the pile had
been heated by the moving air.

We will end this enumeration of phenomena which prove the
generation of heat by mechanical force, by quoting an important
experiment of Davy's; This illustrious physicist, by rubbing two
pieces of well-dried ice together, succeeded in melting a certain
quantity. Now, to explain the disengagement of heat produced by
friction, the partisans of the material theory of heat, who considered
it a fluid contained in the interstices of bodies, reasoned thus :
Friction changes the calorific capacity of different bodies ; it
diminishes this capacity so that the heat which was retained before
the mechanical actions can no longer remain within the body after
the molecular change which agitates it: it is this heat which is
disengaged by friction, and, before latent, now becomes apparent."

The experiment of Davy renders this explanation impossible ; let
us bear in mind that water has double the calorific capacity of ice ;

502 PHYSICAL PHENOMENA. ' [BOOK iv.

after the fusion of a certain quantity of ice, the water produced by it
contains more latent heat than before : hence it would be impossible
to understand, in accordance with the material theory, whence the
heat proceeds which has caused the ice to pass into water. From
this it is concluded that the mechanical force brought into play
in friction is transformed into heat, — that is to say, into a force of
another kind : that there is transformation of visible motion into
molecular or atomic motion.

Percussion and compression develop heat like friction. Thus,
when a nail is driven into a piece of wood with a hammer, not only
is the nail heated, an effect which could result partly from the friction
against the wood, but the hammer itself undergoes an elevation of
temperature. An iron bar, beaten with successive strokes, can be
made red-hot. Plates of gold, silver, and copper, compressed under
the coining press which is used to stamp money, become heated, but
the elevation of temperature is not the same in different metals.
Generally speaking, the quantity of heat developed by mechanical
action depends on the nature of the substances submitted to these
actions, on the state of their surface, and on the pressure exercised.

The compressibility of liquids is very slight: nevertheless, by
submitting liquids to considerable pressure — for example, of from 30
to 40 atmospheres — the disengagement of heat can be established.
Very great compression can be effected in gases, and a considerable
elevation of temperature can be obtained, when a gaseous mass is
suddenly compressed into a limited space. This fact illustrates the
principle of the pneumatic syringe which we have described in the
First Book of this work. The expansion of a gas produces an effect
contrary to that of compression,^-that is to say, a fall of temperature
results ; carbonic acid gas, first liquefied by compression under 40 or
50 atmospheres in a receiver, produces so much cold by expansion on
escaping into the air that it passes into the solid state ; and then
takes the form of flakes, white as snow, of solidified carbonic acid.
Their temperature is then 93 degrees below zero Centigrade.

The same phenomenon of cooling takes place, when steam issues
in a jet from the valve of Papin's digester. Its sudden expansion is
accompanied by a cooling which condenses it as mist : on plungiDg
the hand into the jet of steam, a sensation of coolness is felt which
at first seems strange. Great care must be taken in this experiment

CHAP, vii.] SOURCES OF HEAT. 503

when the vapour contained in the boiler has only the ordinary
atmospheric pressure ; on escaping into the atmosphere, at this
pressure, it retains the temperature of 100° C., and the hand may be
terribly scalded.

In order to complete what we have said concerning heat-sources,
we have to mention those which life maintains in organized beings,
vegetable and animal. It seems to be proved that animal and vege-
table heat has its origin in a series of chemical actions more or less
complex, which constitute the phenomenon of nutrition, respiration,
and assimilation of food.

504 PHYSICAL PHENOMENA. [BOOK iv.

CHAPTEE VIII.

HEAT A SPECIES OF MOTION.

What we understand by the mechanical equivalent of heat — Joule's experiments
for determining this equivalent — ^Reciprocal transformation of heat into
mechanical force, and of mechanical force into heat — Heat is a particular
kind of motion.

IN the study of the science of heat, we have considered two
classes of phenomena. On the one hand, we have described
the many effects produced by the variations of heat in bodies ;
and, on the other, we have reviewed the different processes by which
heat can be engendered. We have now to indicate the relations
which exist between these two orders of phenomena, the reciprocal
dependence of which, being now proved, constitutes the mechanical
theory of heat.

We have seen that one of the effects of heat is to expand bodies,
that is to say, to produce molecular movements which increase the
distances of the molecules from each other; and, thus considered,
expansion is nothing more than a mechanical effect. When the
increase of heat attains a certain limit, there is a change of state, a
passage from the solid to the liquid condition, and from the liquid
to the gaseous : this is also a mechanical effect, for it does not appear
doubtful that these modifications in the aspect of a substance are due
to variations in the respective distances of the molecules, and after-
wards in the actions which they exercise on each other. We have
also seen that increase of heat confers on vapours and gases the elastic
force which, in modern machines, so advantageously replaces the old
motive forces. In all these cases, heat is transformed into mechanical
work ; or, in other words, a certain quantity of heat is consumed in

CHAP, vni.] HEAT A SPECIES OF MOTION. 505

producing work, although in many cases this work is not susceptible
of measurement in the present state of science.

It is not less evident, however, that whenever heat is pro-
duced, a certain quantity of work is expended ; this is most
certain in the case of heat engendered by friction, percussion, and
compression : that which is disengaged by chemical action is
f believed to be produced by the molecular movements which con-
stitute the combinations.

This relation between the forces which give rise to the pheno-
mena of heat and the other mechanical forces, had been long sus-
pected : but it was reserved to our own time to transfer it from a
state of vague hypothesis to that of a theory proved and verified by
experiment. Dr. Mayer, of Heilbronn, a little town in Germany, had
the honour of giving the first definite formula to the theory and of
developing the consequences : in 1842 he calculated the mechanical
equivalent of heat, which was experimentally determined a year later
by an English physicist, Dr. Joule, who was at that time unacquainted
with the researches of the German physicist. Mayer's theory was not
however satisfactory, and the real honours of the discovery undoubt-
edly belong to Joule.

Many other physicists may be referred to as having aided to
establish the theory; it will be sufficient for us to mention MM.
Kegnault and Him in France, Clausius in Germany, Thomson, Clerk-
Maxwell, and Rankine in England.

We will now endeavour to give an idea of the mechanical
equivalent of heat, and of some of the experiments by which it
has been determined.

Let us first recall to mind the meaning of the term work
in mechanics. When a power is employed in a machine in motion
to overcome a resistance with which it is in equilibrium, it has been
proved that there is always an equality between the products obtained,
by multiplying, on the one hand, the power by the path passed over
by its point of application ; and, on the other hand, the resistance
by the path over which the point of application of this latter passes.
For example, if a power equal to 10 kilogrammes produces equili-
brium with a resistance of 30 kilogrammes, and the path traversed
by this according to its direction be 1 metre, the path traversed
by the power during the same time will be 3 metres ; there will then

506

PHYSICAL PHENOMENA.

[BOOK iv.

be equality between the two products 10 x 3 and 30 x 1. The name
of work is given to each of these products ; the first is work spent on
the machine, and the second work done by the machine. It is con-
venient to take as a unit of work or dynamic unit, the work developed
by raising a weight of 1 kilogramme to a height of 1 metre. This
unit is designated a kilogram-metre. On the other hand, we have seen
that quantities of heat are measured in calories ; by calorie is under-
stood the heat necessary to raise from 0° to 1° Centigrade the tempe-
rature of 1 kilogramme of water. The problem which presented
itself to 'physicists was : To determine by experiment and calculation
the number of kilogrammetres necessary to engender the quantity of
heat represented by a calorie. (English men of science use a different
unit, called a foot-pound, instead of a kilogrammetre.)

FIG. 328.— Joule's experiment. Determination of the mechanical equivalent of heat.

We deal first with the heat which raises 1 kilogramme of water
1° C., and then determine the mechanical work necessary to produce
the same result.

It is this number which Mayer and Joule have called the mechan-
ical equivalent of heat. The experiments which have been made
with a view of determining this important number consist essentially
in the production of a certain quantity of heat by the aid of
mechanical action, and in measuring carefully the heat produced,
and the work consumed in the operation, of course taking into

CHAP, viii.] HEAT A SPECIES OF MOTION. 507

account losses of heat and of mechanical work. The following are
some of Joule's experiments.

He compressed air, by means of a force-pump, into a metallic
vessel in the water of a calorimeter. After a certain number of
strokes of the piston, the pressure of air having attained a certain
number of atmospheres, he observed the elevation of temperature
of the water, and deduced from it the quantity of heat communi-
cated to it. The heating was not entirely due to the compression
of air, but also to the friction of the piston. He therefore re-
commenced the operation by allowing the receiver to communicate
with the atmosphere, that is to say without compressing the air.
The heat produced by this fresh operation was evidently due to
the friction in the first operation. Joule found by this method
444 kilogrammetres for the mechanical equivalent of the heat.

By turning a paddlewheel in water or in mercury (Fig. 328),
the same physicist observed the elevation of temperature of the
liquid, and likewise deduced the number of calories caused by the
friction. On the other hand, he easily measured the work expended
in producing the rotation. The final result arrived at by Dr. Joule
gives, as the mechanical equivalent of heat, 772 foot-pounds ; that
is, the force expended in raising 1 pound through 772 feet will raise
the temperature of the pound of water 1° F.

To sum up, it has been shown by a great number of experiments
made by various physicists, that the mechanical equivalent of the
heat necessary to raise 1 kilogramme of water 1° C. is about
425 kilogrammetres. Or, according to the definition given above,
that the quantity of heat necessary to raise the temperature of a
kilogramme of water 1° C. is capable, if it could be entirely ex-
pended in mechanical work, of raising a weight of 425 kilogrammes
to a height of one metre, or 1,390 pounds, to the height of a foot.
Eeciprocally, when work equal to 425 kilogrammetres is completely
transformed into heat, the heat produced is capable of raising the
temperature of a kilogramme of water 1° C. Thus the transforma-
tion of mechanical force into heat and of heat into mechanical force,
is not only a fact acquired by science, but an important demon-
stration which throws light on the nature of the cause to which
we must attribute the phenomena which we have studied in this
Fourth Book.

508 PHYSICAL PHENOMENA. [BOOK iv.

The study of the laws of radiant heat had already induced us to
assimilate heat-waves with luminous waves, and to regard heat itself
as produced by certain vibrations of the ether. In penetrating the
interior of bodies it is probable that the heat communicates to their
molecules certain movements which, transformed in different ways,
sometimes change the volume of the bodies, sometimes modify
their physical condition, and sometimes produce intimate effects
of such a nature as to alter the mode of association of the
elementary atoms. These movements, on being propagated by our
nerves, produce in us the sensation of heat.

BOOK V.

MAGNETISM.

BOOK V.
MAGNETISM.

CHAPTEE I.

MAGNETS,

Phenomena of magnetic attraction and repulsion — Natural and artificial magnets ;
magnetic substances — Poles and neutral line in magnets — Action of magnets
on magnetic substances ; action of magnets on magnets — Law of magnetic
attraction and repulsion — Direction of the magnetic needle ; declination and
inclination ; influence of the terrestrial magnet — Process of magnetization —
Attractive force of magnets.

II /TINEKALOGISTS gave the name of magnetic oxide of iron, or
-LT-L magnetic iron, to an ore of this metal, which is found in large
quantities in the mines of Europe and America, particularly in
Sweden, in the Isle of Elba, and in the United States. It was
worked for some time at Bona (Algeria) ; and lastly, according to
ancient writers, it was formerly found in Asia Minor, near the two
towns of the same name of Magnesia. The mineral to which we
refer is composed of protoxide and sesquioxide of iron ; its colour
is generally black or brown, and sometimes greyish, with a metallic
brightness. Some specimens possess the property, known to the
ancients, of attracting pieces of iron which are placed near one of
their points : these are natural magnets, or, as they are more commonly
called, lode-stones. We shall presently see how the attractive power
of the natural magnet can be communicated to tempered steel: the
pieces or bars of steel thus prepared are called artificial magnets.

512 PHYSICAL PHENOMENA. [BOOK v.

Iron is not the only substance capable of being attracted by a
magnet ; the same effect takes place with other metals : cobalt, nickel,
chromium and manganese, cast iron, steel, and all specimens of
oxidized iron, which are not themselves magnets, are also attracted.
These bodies are ranged under the same head of magnetic substances}-
The phenomena which we are about to describe remained unknown
for centuries, like those of electricity ; yet the ancients were aware
of the two .principal facts which, in the hands of modern observers,
have been the starting-points of these two branches of physics which
are now united. The attraction of light bodies by yellow amber,
and the attraction of iron by the lode- stone, were only amusements
in their eyes, or singularities of nature ; in the present day they are,
among thousands of others, two particular manifestations of an
agent unusually diffused through, and continually in action in, the
physical world.

The attractive power of magnets, natural or artificial, for magnetic
substances is easily proved. The following are some of the processes
used for this purpose : —

If a magnet is immersed in a quantity of iron filings, we observe
on removing it that at certain parts of its surface numerous particles

of the metal are attached in the
form of tufts (Fig. 329), and on
placing small pieces of iron, such as
nails, near the same points, they
will be seen to move forward to
the magnet, and to adhere with a

FIG. 329,-Attraction of iron filings by a natural f°rC6 the Strength of which Can be

determined by the effort neces-
sary to remove them. By means of the magnetic pendulum, which
consists of an iron ball or any other magnetic substance suspended

1 The words magnetism and magnetic come from one of the Greek names of
the magnet, fiayvrjTrjs, which the ancients themselves believed to be derived from
the names of the two towns of Magnesia in the neighbourhood of which lode-
stones were first found. Aristotle called the magnet simply \i0os, the stone, par
excellence. It was also termed Lydian stone, Hercules stone — rjpan\fia \i6os.
According to M. Th. H. Martin, this last term was wrongly interpreted as
synonymous with the Heraclea stone, one of the names of the town of Magnesia,
which induced the ancients themselves to give the name of fjLayvr'jTrjs to the magnet ;
which name the Romans retained.

CHAP. I.]

MAGNETS.

513

by a thread, the attraction which the magnet exercises on the sub-
stance is even more easily proved. The same apparatus also
shows that the attraction, which is nil at the points where the iron
filings are not attached, is at a maximum where the largest tufts
have been formed. Moreover, the attraction of magnets for magnetic
substances is reciprocal. Thus, a piece of iron brought near a mag-
netized bar rendered moveable by being suspended, as represented
in Fig. 331, attracts the bar, and causes it to move round the axis
of suspension.

This last experiment also proves that magnetic attraction is
exercised at a distance, and increases in intensity as the distance

FIG. 330.— Magnetic pendulum.

diminishes ; we shall see further on in accordance with what law this
takes place. But at the same distances this action is scarcely
weakened by the interposition of bodies, either liquid or solid, pro-
vided they are not magnetic. Thus when a magnet is moved beneath
a sheet of paper, or cardboard, a plate of glass, wood, or porcelain,
pieces of iron placed on the surface of these sheets or plates will
follow the motion of the magnet.

Although magnets, either natural or artificial, and magnetic
substances, are reciprocally attracted, this does not prove that the
properties of both are alike. There is an important difference, which

R R

514

PHYSICAL PHENOMENA.

[BOOK v.

we must observe, viz. that substances which are simply magnetic do
not attract each other : a piece of iron which attracts a magnet has
no action on iron, if it is not in the vicinity of a magnet. There
is another important difference, viz. that a piece of iron undergoes
attraction at all points, whilst in a magnet the attractive property
is unequally distributed : we have already seen that it does not exist
at certain points and is at maximum at others. The experiments
which follow will show this characteristic difference between magnetic
substances and magnets.

FIG. 331. — Attraction of a magnetic bar by iron.

By examining a magnet which has been placed in iron filings
(Fig. 329), the latter are not only seen to be attached more particu-
larly to the two opposite parts, but the arrangement of the particles
takes a special direction, as if in each part where the attraction is
strongest there were a centre of attraction. Towards the middle
of the bar, on the contrary, a part will be noticed where no particle
of iron has attached itself. The two extreme points of the magnet are
called the poles, and the middle section of the magnet the neutral
line or equator. The following is an experiment which shows in a still
more striking mariner the existence of the poles and the neutral line : —
On the bar which serves as a magnet a sheet of cardboard is placed,

CHAP. I.]

MAGNETS.

515

upon which very fine iron filings have been sifted. The particles are
now seen to dispose themselves in a regular manner round the poles
of the magnet, and to form lines which are convergent and symmetrical
with respect to the neutral line ra m (Fig. 332). Sometimes a magnet

FIG. 332. — Magnetic figures. Distribution of iron filings on a surface.

possesses more than two poles : besides the extreme poles, the existence
of which we have proved, intermediate points are observed to which
the iron filings attach themselves, and which are also separated from

FIG. 333.— Consequent points, or secondary poles of magnets.

each other by neutral lines, as is shown in the. magnetic figures repre-
sented in Fig. 333. These are called consequent poles. It is easy
now to explain the difference which exists between magnets and
magnetic substances. The latter have neither poles nor neutral lines :
whichever of their points is presented to the poles of a magnet there

R I? 2

510 PHYSICAL PHENOMENA. | BOOK v.

is always reciprocity of attraction, whilst a magnet acts only at
its poles.

Let us take two or more magnetic bars and suspend them at their
centres, and successively approach the two poles of any one of them
to the two poles of the others ; we observe, on presenting a given pole
of the first to the two poles of the second magnet, that attraction takes
place by one of them and repulsion by the other : the same pheno-
mena will take place with the others. All the poles attracted by
the pole M of the trial bar are said to be poles of the same name ; let
us mark them with the letter A : while all the poles repelled by the
same pole M are also poles of the same name, because on them the
action is in the same direction under the same circumstances ; let us
mark them with the letter R. If now the opposite pole N of the trial
bar is presented to each of the poles of the other magnetized bars, it
will be found that it repels all the poles A and attracts all the poles R :

thus in every way the two opposite

poles of the same magnet are poles
of contrary names. Let us see now
how two poles of the same name
act on each other : to this end we
will place near each other any two

FIG. 334.— Attraction and repulsion of the J

poles of magnets. 0£ ^Q p0"[es ^, or again any two of

the poles R ; in both cases we shall find that they repel each other.
If, on the contrary, we present two poles of contrary names, a pole
A and a pole R, they will be seen to attract each other; which
proves that in the preceding experiment the pole M of the trial bar
is of the same name as the poles R, and the pole N of the same name
as the poles A.

We may sum up these observations as follows : —

Opposite poles of the same magnet are of contrary names; if the
fiction of one of the two on a given pole of a magnet is attractive,
the action of the other is repulsive.

The poles of the same name of any two magnets repel each other,
while poles of contrary name attract each other.

We here have a distinction which radically separates magnetic
substances, such as soft iron, from artificial or natural magnets, and
enables us to determine whether a steel bar or a specimen of oxide of
iron is a magnet or not. It is sufficient to observe in what manner a

CHAP. I.]

MAGNETS.

517

magnet comports itself in the presence of the bar, or of a piece of
lodestone. If there is attraction at every puint, it is not a magnet ;
but if there is attraction at one extremity and repulsion at the other,
it is a magnet, not simply a magnetic substance.

Magnetization is the condition of a substance which has the pro-
perty of attracting iron and other magnetic bodies, and which sub-
stance possesses two poles and a neutral line. This property may be
permanent or temporary : it is permanent in natural magnets or steel
bars magnetized by processes of which we shall soon speak. The
following experiment proves that it is temporary in magnetic sub-
stances which are in contact with one of the poles of the magnet : —

A small cylinder of soft
iron can be raised by
means of a magnet ; this
is magnetized by the influ-
ence of the magnet, for on
approaching a second cylin-
der of iron to its extremity,
it undergoes an attraction
and is also raised. Thus
what is called a magnetic
chain can be formed at the
end of the bar, composed of
pieces of iron which attract
and support each other.
But if the magnet in con-
tact with the first piece of
soft iron is removed, in an

instant all the others fall, thus losing the temporary magnetism with
which the presence of the magnet had endowed them. Each piece
of soft iron becomes for the time being a magnet with two poles and
a neutral line, and this is proved by the fact that if magnetic figures
are formed during the contact of the magnet and the iron cylinder,
the iron filings arrange themselves in a manner which corresponds
to that of the magnet itself. It will also be noticed that the neutral
line is nearer the pole next to the magnet than to that which is
more remote. Magnetic attraction does not require absolute contact ;
it is only necessary that the distance be sufficiently small between

FIG. 335. — Magnetization by the influence of magnetism.

518 PHYSICAL PHENOMENA. [HOOK v.

the pole of the magnet and the piece of soft iron which momentarily
acquires the polar magnetism, and the distance depends on the
strength of the magnet employed.

»*9m

--•

FIG. 336. — Magnetization by influence at a distance.

When a magnetic bar is broken into two or more pieces, each
piece, however small it may be, becomes a complete magnet with two
poles and a neutral line ; only, its magnetic power is no longer so
strong as in the first magnet, as may be proved by the weights of
soft iron which eacli is competent to lift. The magnets which
proceed from this rupture have their poles of contrary names
end to end ; that is to say, situated at the two extremities of the
pieces near each other which were joined before the rupture, as in
Fig. 337.

l> (I ,
FIG. 337. — Rupture of a magnet; disposition of the poles in the pieces.

A magnetic needle is a lozenge-shaped piece of steel endowed with
the property of a common magnet ; that is to say, having a pole at
each extremity and a neutral line at its centre. A magnet of this
kind suspended horizontally in a loop of paper by an untwisted
fibre of silk, or well mounted on a pivot with an agate centre
(Fig. 338) in such a way that it can turn freely in every direction,
after some oscillations always assumes a certain direction in a
horizontal plane ; at least, it undergoes variations of but slight
amplitude.

CHAP. 1.]

MAGNETS.

519

This property of the magnetic needle to turn one of its poles
towards the northern horizon, has been utilized for centuries by
navigators.1

It is not often, however, that the needle turns to the true North,
so that the vertical plane passing through its poles does not coin-
cide with the meridian plane of the
place. The angle of the two planes
is called the declination of the mag>
netic needle, or, simply, declination.
We shall see, when speaking of ter-
restrial magnetism, that the declina-
tion is not the same in esrery part
of the world ; in some places it is
nil, in other regions it is to the
east and in some to the west : more-
over, in the same place it varies
in the course of centuries. At the
present time, at Paris, the declina-
tion is west, and about 18° 30', that
is to say, the vertical plane passing
through the poles of the magnetic needle — a plane called the mag-
netic meridian — makes with the geographical meridian plane an
angle of 18 degrees and a half, At London this declination is
about 21°. One of the poles of the needle is turned nearly to the
N.N.W. This constancy of direction, in freely suspended magnets
in a horizontal plane, may be simply put to the test by a mag-
netized sewing-needle. On placing it on a cork float on water
perfectly at rest, the needle assumes the direction of which we
have just spoken. Moreover, between the two poles of the needle
there is a very characteristic difference ; for if, when the needle is
in equilibrium, it is turned end for end, it does not keep its new
position, when even the direction which has -been given to it is

1 It appears certain that from the second century before the Christian era, the
Chinese used compasses indicating the direction of the South. These compasses
carried a little statuette, which turned on a vertical point, the extended arm of
which always pointed to the South, because it contained a magnetic needle, whose
south pole was towards the hand and the north pole towards the elbow (Th. H.
Martin). The compass with a balanced needle was known to the Arabs, who
doubtless transmitted it to Europeans about the twelfth century.

FIG. 338. — Magnetic needle.

520

PHYSICAL PHENOMENA.

[BOOK v.

FIG.

;9.— Magnetic declination in
Paris, October 18C4.

identical with the first ; it will be seen to turn on itself, describe a
semi-circle, and again assume its original position, so that the same
pole is always turned to the North.

If instead of placing the magnetic
needle so that it can turn freely in a
horizontal plane, it is suspended by its
centre of gravity round a horizontal axis,
it will be able to turn freely in a vertical
plane. Let us suppose this plane the
magnetic meridian. Then the one of the
two poles turned towards the north is
inclined, and dips below the horizon,
making with this plane an angle which
is called the magnetic inclination. In some parts of the earth,
near the equator, the inclination is nil ; it increases generally in
proportion as the latitude increases, and near the poles there are
points at which it is at a right angle : the magnetic needle there
assumes a vertical position ; these are the magnetic poles of the earth.
At Paris, the inclination, which varies slightly from year to year,
is at the present time about 66°.

A magnetic needle may be arranged so that it places itself in
the magnetic meridian with an inclination to the horizon such
as we have just stated. Fig. 341 shows an arrangement which
allows the needle to turn on a horizontal
axis passing through its centre, and can
then take up the local dip as the axis
is suspended by a thread. The system
begins by oscillating, until the needle is
in the magnetic plane, and then it dips
to an extent equal to the inclination at
the place. Elsewhere we shall have
occasion to describe the instruments by
which we accurately measure the inclina-
tion and declination of the magnetic needle : to these instruments
the name of magnetometers has been given.

These experiments prove to us that the terrestrial globe exercises
an influence on a magnet similar to that which one magnet exercises
on another. It is just as if, at the interior of the earth, there existed

FIG. 340. — Inclination of the needle
at Paris, October 1864.

CHAP. I.]

MAGNETS.

521

a powerful magnet possessing two poles. Physicists have stopped
at this hypothesis, which, moreover, does not imply the existence of
a material mass analogous to the natural magnets, and lying in the
deep strata of our spheroid, as
we shall see when we study
the relations which exist be-
tween magnetic and electric
phenomena. If the earth is
compared to a magnet, the pole
in the northern hemisphere will
naturally be called the northern
magnetic pole, and that in the
southern hemisphere the south-
ern magnetic pole. But, from
the preceding we have learnt
that poles of contrary names
attract each other, while those
of the same name repel each
otherj.it follows, therefore, that
the pole of the magnetic needle
which turns to the north is the

southern pole of the needle, whilst the pole turned towards the
south is its northern pole. When the position of the needle has
only to be considered, its southern pole is called the north pole,
and its northern pole the south pole. But if the law of the mutual
action of the two magnets is well understood, their denominations
cannot be equivocal. *\

The inclination and declination of the magnetic needle are subject,
in different regions of the globe, to variations, some of which are
periodical whilst others appear to be irregular. Sometimes even the
needle undergoes perturbation, as if the terrestrial globe was the
seat of real magnetic storms ; then we see towards the polar regions
luminous phenomena, visible at great distances, known as the
northern or southern auroras. The frontispiece represents a polar
aurora observed in the north of the Scandinavian peninsula. We
shall give a description of this phenomenon in Book VIL, devoted to
atmospheric meteors.

8 S

FIG. 341.— Magnetic needle, showing both the
inclination and declination.

522

PHYSICAL PHENOMENA.

[BOOK v.

Hitherto we have only spoken of the direction of the actions
which magnets exercise on each other, or on magnetic substances.
The intensities of the forces of attraction and repulsion which reside
in the poles of magnets have also been measured. For this purpose
Coulomb used an instrument similar to the torsion balance, which
enabled him to measure these forces ; this is the magnetic balance
represented in Fig. 342.

FIG. 342. — Coulomb's magnetic balance.

A long magnetic bar is suspended by a metal thread placed so
that it is in the magnetic meridian without any torsion of the thread :
if the thread is now turned in such a way as to throw the bar out
of this first position, and to cause it to make a certain angle with
it, the force of torsion will be equivalent to the intensity of the
action of the terrestrial magnetism which tends to bring back the
bar into the magnetic meridian. Coulomb commenced by assuring
himself that this intensity is proportional to the angle of displace-
ment of the bar, for small deviations. If we then place vertically
at the side of the instrument, as shown in the figure, another
magnet in the magnetic meridian (shown by the dotted line), and
in front of the pole of the same name, repulsion ensues: the sus-

CHAP, i.] MAGNETS. 523

pended magnet turns until a position of equilibrium is attained.
The repulsive force of the two magnets is measured by the sum of
the two forces, the terrestrial magnetic force on the one hand, and
the force of torsion developed in the thread on the other. If now,
by the rotation of a micrometer situated at the upper part of the
instrument, the two poles are gradually brought nearer together,
and if, at each operation, the intensity of the repulsive force is
measured, the law which Coulomb discovered will be proved : it
is as follows : —

Magnetic repulsions vary in the inverse ratio of the squares of the
distances through which they are exercised.

By another method, which consists in counting the number of
oscillations which a magnetic needle makes when one of its poles is
placed in the presence of the pole of contrary name of another
magnet, at different distances, Coulomb proved that the same law
of variation in inverse ratio of the squares of the distances, applies
to magnetic attractions as well as to repulsions. We shall hereafter
find that it also governs electrical forces.

At the commencement of this chapter we said that masses
of steel are capable of acquiring the properties of natural mag-
nets. To obtain this result several
processes are used, which we shall
now describe.

The oldest mode of magnetization ^H, ^

is that of single touch, which consists ** r ^ *

in placing the pole of a magnet in con- F'°-
tact with one of the extremities of a

tempered steel bar. After a certain time the bar is found to be mag-
netized, with a pole at each of its extremities. A more powerful
magnetization is obtained by passing the magnet several times
from one end to the other of the bar which is to be magnetized
(Fig. 343). The touching ought always to be done with the same
pole and in the same direction. The pole' a, obtained at the
extremity at which the movement begins, is of the same name
as the pole A of the magnet which is placed in contact with the
steel bar.

There are several methods of magnetization — discovered about

s s 2

524 PHYSICAL PHENOMENA. [BOOK v.

the middle of the last century — which are distinguished from the
first by the term of double touch, because two magnets are used
instead of one. We shall only describe the methods of ^Epinus
and of Duhamel.

The bar to be magnetized, a &, is placed with its two extremities
on the contrary poles of two powerful magnets, A7 B'. Two other

FIG. 344. — Magnetism by separate double touch. Duhamel's process.

magnets, A, B, are then taken, which are inclined from 25 to 30
degrees over the middle of the bar, the two contrary poles are placed
opposite to each other, and care is taken that each of these poles is
on the side of the pole of the same name belonging to the fixed
magnets A' B'. If the movable magnets are passed in the opposite
direction several times without changing their inclination, the polar
magnetism is developed in the steel bar, which acquires two poles,
a I, of contrary names to the poles B B', A A' of the magnets used.
This is Duhamel's process ; it gives powerful magnetization, but not
at all regular, and it sometimes produces consequent points. The
process of ^Epinus only differs from that of Duhamel by the two
movable magnets being inclined from 45 to 50 degrees, and after
having placed them in contact and bound them together at the
middle of the steel bar, both are passed together from one extremity
of the bar to the other. The magnetization thus obtained is not only
more powerful than the preceding, but more regular. Therefore the
separate double touch is preferred when needles are to be magnetized
for compasses.

Steel, or even- soft iron bars, can be magnetized without the use
of artificial or natural magnets, if they are placed and kept for some
time in the plane of the magnetic meridian and in the direction of the
inclination. In this position a steel bar is magnetized along its whole
length, and obtains all the properties of a magnet : a bar of soft iron
becomes a magnet, but only a temporary one ; the magnetic action of
the terrestrial globe magnetizes by influence, or induction as it is

CHAP. I.] MAGNETS. 525

called. If one of the extremities of a magnet thus produced is
struck with a hammer, the magnetic force of the bar is not only
increased but it becomes permanent.

Pieces of wire strongly stretched whilst held in the direction of
the dipping needle are magnetized ; and if they are united by their
poles of similar name in a single sheaf, a very powerful magnet may
be obtained. To magnetize by the action of terrestrial magnetism,
it is sufficient to hold the bar of iron or steel vertical while one
of its extremities is struck with a hammer. In this manner this
bar is in the plane of the magnetic meridian, but without the in-
clination of the magnetized needle.

This action of the earth well explains how it happens that in
shops in which steel and iron are worked, a great number of tools
become magnetic, shovels, pincers,
iron-work of windows, and generally
all the pieces of iron- work which are
a long time in a position perpen-
dicular to the horizon ; this is also

the case with the crosses which FlG_ 345._Magnetization by the method
surmount church towers. We shall of ^pinus-

soon have occasion to speak of the magnetism obtained by electric
currents, but it was known for a length of time that lightning could
communicate magnetic properties to iron. In the article Magnet
in D'Alembert and Diderot's Encyclopaedia we read: "One day
lightning entered a room in which there was a box of steel
knives and forks destined for sea use ; the lightning entered by
the southern angle of the room, exactly where the box was
placed; several knives and' forks were melted and broken; others
which remained whole were strongly magnetized, and became com-
petent to lift large nails and iron rings, and this magnetic virtue
was so strongly impressed that it was not dissipated when they
became rusty."

The strength of magnets alters in the course of time : shocks,
changes of temperature, and lastly the action of the earth are the
causes of this alteration. The strength depends on the volume of
the magnet, its form, and the temper of the steel; thus, in two
similar magnetized bars, the magnetic intensity is sensibly propor-
tional to their size, or, in other words, to cubes of equal dimensions ;

526 PHYSICAL PHENOMENA. [BOOK v.

nevertheless, it has been noticed that small magnets are, in pro-
portion, more powerful than large ones: some have been made
which supported pieces of iron whose weight was a hundred times
their own. This suggested the idea of forming magnets by uniting
a series of magnetic bars by their similar poles : these are called
compound magnets. Fig. 346 shows how these magnets are arranged.
In the Koyal Institution of London there is a compound magnet
formed of 450 plates, each of which is 2 feet in length. It is
sufficiently powerful to lift 110 Ibs.

Form also influences the strength of magnets ;
thus, with equal weights, a lozenge-shaped mag-
netic needle is more powerful than a rectangular
bar.

The temper of the steel has a great influence
on the force of the magnetized bar : tempered
steel is magnetized more strongly than non-tem-
pered steel; if it is subjected to increasing tem-
peratures, the magnetic force is weakened more
and more. Coulomb has shown, however, that the
result is quite different, if, instead of working
with rectangular bars, very fine and long needles
are employed ; in this case heating increases their
magnetic force.

Flnet346fwmedlpofDtweive Lastly, temperature has a great influence on
magnettoban. tlie force of magnetSf A magnetic bar when

heated to redness loses all its magnetism, the intensity diminishing
as the temperature rises, as stated by Coulomb. But if the varia-
tions of heat take place within narrow limits, the magnetic in-
tensity varies only slightly, and the magnet resumes in cooling
the strength which it originally possessed. This refers to polar
magnetism, that is to say, to that possessed by magnets ; but it is
also the case with simple magnetic substances like soft iron, nickel,
&c., which also lose their property when their temperature is raised
to a certain degree. Iron is not magnetic if it is heated to a cherry
red-heat, and the same happens in the case of cast-iron heated to
whiteness. Above 350°, nickel is no longer magnetic, and man-
ganese only becomes so below zero, about - 20°. These last results
are due to M. Pouillet.

CHAP. I.]

MAGNETS.

527

We have now to speak of the means employed to preserve the
magnetic force in natural and artificial magnets. Experiment has

proved that magnetic bars, united parallel to m

each other, two by two, in a box, so that
the opposite poles are together, preserve
their magnetism, if care is taken to join
the contrary poles by bars of soft iron,
which are called armatures or keepers.

An armature is used to increase the power
of a magnet. When these are used it is
sometimes curved in the form of a horse-
shoe, the armature uniting the two poles.

A magnet armed in this way (Fig. 347)
carries not only a greater weight than that
which a single pole would carry, but double
that weight. By uniting two rectangular
magnets or compound magnets, turned so
that their opposite poles A, B are joined by a
similar armature (Fig. 348), a very strong
magnet is obtained. Experiments also show
that magnets thus arranged keep their
magnetic force better if they are left armed FlG 347_Ironhorse^hoe magnet,
with their keepers, or if the charge of iron with its armatl
that they are able to lift is suspended on it, always provided that it

Fio. 348.— Magnet formed of two compound bar magnets.

does not exceed that limit ; for then, the keeper being suddenly
detached, the magnetic force of the magnet is weakened.

528

PHYSICAL PHENOMENA.

[BOOK v.

Masses of magnetic oxide of iron, which constitutes natural
magnets, have often but feeble magnetism ; but their magnetic
virtue has been increased by furnishing them with pieces of soft
iron conveniently arranged. Fig. 349 shows how these armatures

FIQ. 349.— Natural magnet furnished with its armature.

are placed : m m are plates of soft iron in which the natural
magnet is enclosed, and which are terminated by thicker masses
pp, these forming real poles to the magnet; c is the armature or
keeper. Finally plates of copper are used to support the plates of
soft iron round the mass of magnetic oxide.

BOOK VI.

ELECTRICITY.

BOOK VI.
ELECTRICITY.

CHAPTEE I.

ELECTRICAL ATTRACTION AND REPULSION.

Attraction of amber for light bodies — Gilbert's discoveries ; electricity developed
by the friction of a number of bodies — Study of electrical attraction and repul-
sion ; insulators, or bad conductors ; good conductors — Electrical pendulum —
Kesinous and vitreous, positive and negative electricity — Laws of electrical
attraction and repulsion — Distribution of electricity on the surface of bodies —
Influence of points.

THE ancients discovered that amber, when it is quickly rubbed with
a piece of woollen stuff, and brought near light bodies such as
bits of straw, pieces of paper, or feathers, causes them to move towards
it, as if attracted by some mysterious force. Thales of Miletus, who
lived 600 years before the present era, mentioned this property ; and
the Greek philosopher, Theophrastus, speaks of jet as likewise possess-
ing it. But to these two facts alone, during more than two thousand
years, the knowledge of physicists was confined, so far as this class of
phenomena is concerned. Pliny the naturalist, on mentioning the first
fact, stated that " friction gives to amber heat and life."

About the year 1600, an English doctor, William Gilbert, to whom
science owes many discoveries concerning the properties of the magnet,
discovered that glass, sulphur, resins, and various precious stones
possessed the attractive properties of amber. Since that time a great
number of physicists have extended the researches of Gilbert, and

532 PHYSICAL PHENOMENA. [BOOK vi.

brought to light many curious phenomena before unknown, and thus
contributed to found the branch of physics which, under the name of
electricity, has now undergone so much extension and is of so much
importance. The word electricity means more particularly the cause,
even now unknown, of the phenomena we are about to describe ; it is
taken from the Greek name of yellow amber, electron (rjXe/crpov).1

Nothing is more easy than to produce the phenomena of attraction
of which we have just spoken. A stick of amber, glass, or resin, is
quickly rubbed with a piece of cloth; if the rubbed parts are held
near pieces of straw or paper, at a small distance, these are seen to
approach the surface of the glass, very much as iron filings are
attracted by the magnet, but as soon as they come into contact with
the rubbed surface the attraction is changed into repulsion, and the
light substances move away. When the substance rendered electric
by friction is passed at a short distance over the face, a sensation is
perceived similar to that of a cobweb coming in contact with it. If
the rod of resin is rather large, and the friction energetic and pro-
longed, a sharp crackling noise is heard, when we place the fingei
very near it, and, if the room is dark, a spark will be seen to pass
between the finger and the nearest portion of the rod. These various
phenomena cease if the hand is passed over the rubbed substance.

A body is said to be electrified so long as it shows in any degree
the properties indicated in these experiments ; it is in its natural
state when it gives no sign of attraction or repulsion.

For some length of time it was imagined that, electrically con-
sidered, all substances must be ranged into two distinct classes : one
comprising those which are susceptible of becoming electric by friction :
the other, those which could not acquire this property. It had been
discovered, in fact, on repeating the preceding experiments with
substances of every kind, that metals, stones, vegetable and animal
matter, and the human body, for instance, do not give rise to the
same phenomena as amber, resins, glass, sulphur, &c. But Gray, a
physicist of the last century, determined the cause of this difference,
and showed that it referred only to the particular conditions under
which the experiments were made.

1 Yellow amber is a kind of fossil resin, which is found in great abundance on
the coasts of the Baltic. It has for a length of time been employed on account of
its beauty of colour and transparency as an ornament in dress and jewellery.

CHAP, i.] ELECTRICAL ATTRACTION AND REPULSION.

533

Indeed, after rubbing a glass tube closed with a cork stopper,
we perceive that the stopper itself is electrified, although the cork
rubbed separately does not give any sign of electricity. Gray studied
this transmission of electricity, and proved that it could take place
through a great distance, through bodies which until then were
considered incapable of being electrified by friction. On the
other hand, this transmission cannot take place with substances
capable of being directly electrified under the conditions previously
stated. It follows from these experiments, that different substances

FIG. 350.— Attraction of light bodies.

possess in different degrees the property of conducting electricity
once developed : bodies which were before considered as only sus-
ceptible of being electrified by friction, are precisely those which
conduct electricity the least — they are lad conductors. Those, on the
contrary, which it had been found impossible to electrify, are good
conductors. The consequences of this new distinction are important,
and we shall see they are proved by experiment. As glass, amber,
resin, &c. are bad conducting bodies, electricity can only be developed
in the rubbed portions ; and this is proved by observation. But if they
are touched by the hand, which is a good conductor like the rest of the
body, electricity passes to the latter, then to the ground, and disappears
always at the points where contact takes place. We have seen that it

534 PHYSICAL PHENOMENA. [BOOK vi.

quite disappears if the hand is passed over the whole surface of the
electrified rod. When a metallic cylinder is rubbed, it will be under-
stood that no sign of electricity can manifest itself; and, indeed, as
metals are excellent conductors, if electricity is produced, it instantly
extends over the whole surface of the metal, and, through the inter-
vention of the body of the operator, passes to the ground. If a
handle made of some bad conducting body, glass for instance, is fitted
to the metallic cylinder, and if this handle is held in the hand whilst
the metal is being rubbed, the latter becomes electrified and acquires
the properties which we have described above as belonging to glass,
resin, and amber. For this reason the name of insulating bodies is
given to bad conductors ; by insulating any substance whatsoever, it
becomes susceptible of being electrified by friction.

These experiments can be repeated under a variety of forms.
A person standing on a stool with glass legs is electrified when he is
rubbed with the skin of a cat ; on placing the finger near any part of
his body sparks will pass from him, and during the whole time of
electrization he perceives a singular sensation on the face, like that
caused by an electrified rod.

Water is a good conductor ; and in the state of vapour it possesses
the same property. This is the reason why great care must be
taken when electricity is being obtained, not only to insulate the
substance operated upon if it is a good conductor, but to wipe and
dry the handle or glass supports, or other insulators. This is also
the reason why electricity is produced with greater facility in dry
than in damp weather ; the room in which the experiments are
made must be dried as much as possible previously, so that
the air which it contains may contain as little aqueous vapour as
possible. To avoid the escape of electricity by the insulating glass
supports which are generally employed in electrical apparatus, they
are covered with a layer of shellac varnish, the surface of which is
not hygrometric like that of glass.

Various substances may be arranged according to their order of
conductibility in two classes, viz. into good and into bad conductors
or insulators, but in each of them the conducting property exists
in different degrees, so that no substance is absolutely without it.
The following table gives a few substances arranged in the order of
their decreasing conductibility : —

CHAP. I.] ELECTRICAL ATTRACTION AND REPULSION.

535

Good conducting bodies.

Metals.

Burnt charcoal.

Graphite.

Acidulated water.

Minerals.

Water.

Vegetable substances.

Animal substances.

Steam.

Powdered glass.

Flour of sulphur.

Bad conducting or insulating bodies.
Ice.

Phosphorus.
Caoutchouc.
Porcelain.
Dry air.
Silk.
Glass.
Sulphur.
Resin.
Amber.
Shellac.

From this it is seen that electrical conductibility is not influenced
by the chemical nature of the substance, so much as by its physical

FIG. 351.— Electrical pendulum. Phenomena of attraction and repulsion.

condition or molecular structure. Thus ice is in the number of the
insulators, whilst water and steam are amongst the conductors.
Sulphur and glass in large masses are bad conductors: but when
reduced to very fine powder they conduct electricity very readily.
Coal in the ordinary state is an insulator, but it becomes a conductor
when calcined ; carbon crystallized, or in the state of diamond, is a
bad conductor, but graphite, which is another mineralogical form of

536 PHYSICAL PHENOMENA. [BOOK vi.

carbon, is a good conductor. Heat has great influence on the electrical
conductibility of bodies ; a high temperature confers this property
upon several bodies which are insulators at the ordinary temperature ;
glass, sulphur, shellac, and gases, are among this number.

We will now return to the phenomena of electrical attraction and
repulsion, and study them in greater detail.

We shall for this employ a very simple instrument, to which the
name of the electrical pendulum (Fig. 351) has been given. It is a little
ball of elder pith suspended by a silk thread to a stand, and is con-
sequently insulated, as silk is a bad conductor. By holding near the
pith ball a rod of electrified resin, we observe that there is first
attraction ; but, so soon as contact has taken place, the ball is
repelled from the resin, and this will continue to be the case even
when the rod of resin is again brought near to it. In this state, the
pith ball is electrified, which is easily seen by holding the finger to it,
for then it is attracted ; on touching it with the hand, after contact
with the resin, it is neither attracted by the finger nor repelled by the
rod of resin ; the electricity which it possessed has passed into the earth,
through the body of the operator. If, instead of using a rod of resin,
an electrified glass rod is employed, the same phenomena manifest
themselves in the order we have just described : there is attraction
and contact, then repulsion. So far, no difference has been observed
between the electricity developed on the resin and that developed on
the glass, when these two bodies are rubbed with a piece of catskin
or silk. But let us suppose that after having obtained the repulsion
of the pith ball by means of the electrified resin, a glass rod electrified
by catskin is brought near the pith ball. The pith ball is now
attracted by the glass as strongly as if, instead of having been pre-
viously electrified by resin, it had remained in its natural condition.
The same phenomena of attraction will be manifested, if, after having
electrified the ball by contact with the glass rod, a piece of resin
electrified by catskin or silk is placed near it.

Thus the electricity developed on the resin and that developed
on the glass by friction of the catskin or silk acts under the same
circumstances, in an opposite manner; for the one attracts the
electrified body which the other repels, and reciprocally. Hence,
electricity was distinguished by the earlier experimenters into two
kinds, and the names given were resinous electricity and vitreous

CHAP. I.] ELECTRICAL ATTRACTION AND REPULSION. 537

electricity. On repeating the preceding experiments with amber,
sulphur, wax, paper, &c., it will be seen that these substances act,
some like the resin and others like the glass ; and it .is then said that
they are charged either with resinous electricity, or with vitreous
electricity. These terms are now abandoned, and for the following
reason : — As all bodies are capable, as we have just seen, of being
electrified by friction, it is clear that if one of the rubbed bodies is
electrified, the other must be electrified as well ; and this is confirmed
by experiment. But it has been shown, besides, that electricity
developed on one of the bodies is not the same as that developed on
the other ; for example, if two discs are taken, one of polished glass
and the other of metal covered with cloth, each furnished with an
insulating handle, and if after they have been rubbed against each
other they are suddenly separated, the glass disc will be found charged
with vitreous electricity, and the cloth with resinous electricity, as
may easily be proved on trying the action which each of them
exercises on an electrical pendulum, the ball of which has been
previously electrified in the same manner in each case.

But this is not all ; it will be noticed that the nature of the elec-
tricity developed on a body changes according to the body with which
it is rubbed ; thus, glass, which we have seen taking up vitreous elec-
tricity when it is rubbed with silk, on the other hand takes resinous
electricity if it is rubbed with catskin. Shellac becomes charged
with resinous electricity if it is rubbed with a catskin or flannel;
while it acquires vitreous electricity if it is rubbed with a piece of
unpolished glass. By retaining the terms we have just used, a
certain confusion may occur, for which reason the names of positive
and negative electricity have been substituted for those of vitreous
and resinous electricity. However, we must not attach to these words
other signification than this : positive electricity is that developed
on glass by rubbing it with silk ; negative electricity is that ob-
tained on resin by rubbing it with catskin. But the method
of action of these two kinds of electricity may be summed up in
two very simple laws : 1st, All bodies electrified either positively
or negatively attract light bodies in their natural state. 2. Two
bodies charged with electricities of contrary names attract each
other : two bodies charged with electricities of the same name repel
each other.

T T

538 PHYSICAL PHENOMENA. [BOOK vi.

There is no exception to these laws, but the conditions of produc-
tion of one or the other kind of electricity are extremely complex ; the
same substance, we have just seen, is sometimes electrified positively
and sometimes negatively, according to the substance with which it
is rubbed. But modifications, often but slightly apparent on the sur-
face of bodies, change the nature of the electricity developed. Thus
polished and unpolished glass, both rubbed with catskin, take, the
first, positive electricity, the second, negative electricity ; two discs of
similar glass rubbed against each other are electrified sometimes in
one way and sometimes in another; heat possesses great influence,
and most hot substances acquire negative electricity.

Many curious experiments have been made as to the conditions
which determine one or the other mode of electrization ; but little is
as yet known as to the causes of these singular phenomena, and the
theories which have been started to explain them have no greater
advantage than to classify the facts, and thus render them more easy
to fix in the memory.

An insulating body, or a bad conductor, can be electrified either
by friction or by the contact of another body already electrified. We
shall soon see another mode of electrization, which consists in develop-
ing electricity, at a distance, by influence or induction. It is in all
cases interesting to know how the electricity is distributed in a body ;
if it spreads itself through the entire mass or only on the surface —
if, in every part where its presence is manifested, it exerts the same
energy — in a word, what is its tension in the different parts of bodies
of different form.

One of the facts which experiment has already revealed to us is,
that in an insulated body, electricity is located on the surface which
has been rubbed, or which has been placed in contact with an electri-
fied body. This is the case with the most perfect insulators ; in bodies
possessing a less degree of insulation, electricity extends to a little dis-
tance round the parts of which we speak. The reason of this fact is
evidently the same as that which makes these bodies bad conductors
of electricity. On the other hand, in good conductors, electricity, in
whatever mode it may be produced, spreads itself almost instantane-
ously over the whole surface. Experiments which we are about to de-
scribe prove that it does not penetrate into the mass of the body, or,
at least, that the thickness of the electrified stratum is very small.

CHAP. I.]

ELECTRICAL ATTRACTION AND REPULSION.

539

A metallic sphere insulated on a glass foot is covered with two
thin hemispherical envelopes, which are held in contact with it by
two insulating handles ; the whole system is then electrified, and both
hemispheres are suddenly withdrawn. On separately presenting to
the ball of an electrical pendulum, first the sphere itself, then each of
the coverings, we shall observe that these latter are alone electrified.
The electricity was not therefore spread out to a greater thickness
than that of the envelopes. A hollow metallic sphere, pierced with a
hole at the top and placed on an insulating stand (Fig. 353), is charged

Fm, 352. — Distribution of electricity on the surface of conducting bodies.

with electricity ; and in order to ascertain the manner in which the
electricity is distributed, a small gilt paper disc is used, furnished with
an insulating handle — this is called a Carrier QT proof plane— and it is
applied to any point of the outer surface of the electrified sphere : it
is then found that it attracts the pith ball of the electrical pendulum.
The proof plane is now touched with the hand ; the electricity with
which it was charged passes away, and it returns to its normal con-
dition : if it is now applied to the interior of the sphere, care being
taken that it does not touch the sides of the hole, no sign of elec-
tricity will be shown on withdrawing it and presenting it to the pith

T T 2

540

PHYSICAL PHENOMENA.

[BOOK vi.

ball. The result will be the same if the interior of the sphere is first
touched. Faraday made the same experiment by giving to the body
the form of a cylinder of metallic network, which he placed on an
insulated disc of brass ; the disc was then electrified, and he proved,
by the help of the proof plane, that the electricity was located alone
on the outer surface of the vessel.

The same illustrious physicist also made the experiment with a
conical bag of muslin, attached to an insulated metal ring : the latter
is electrified ; and a double silk thread, fixed to the top of the cone,

FIG. 353.— Distribution of electricity on the surface of bodies.

enables the bag to be pulled inside out, and it is always found that the
electricity is on the outer surface, so that it passes alternately from
one surface of the bag to the other (Fig. 354).

Thus it is entirely on the outer surface of conductors that elec-
tricity is distributed : at least, if it penetrates into the interior, the
thickness of the electrified stratum is extremely small. Let us take
two spheres, one plain and of metal, the other of shellac, gilt on the
outside, both being of the same diameter; and then electrify the
first, and measure the electric tension by means of an instrument

CHAI>. i.J ELECTRICAL ATTRACTION AND REPULSION. 541

called an electrometer. If the spheres are now placed in contact,
the electric tension on each of them is found to be half what it
was at first on the single metallic sphere. As the thickness of the
electric stratum on the shellac sphere is equal to that of the gold
leaf, we must conclude that its thickness is not greater on the
solid sphere.

We have just spoken of electric tension. It is the intensity of
the force with which a given portion of the surface of an electrified
body attracts or repels an electrified body exterior to it. Coulomb,
under the name of the electric balance, devised an instrument which
is used to measure this tension, and by means of it he determined the

FIG. 354. — Faraday's experiment to prove that electricity is located on the
outer surface of electrified bodies.

laws according to which electric attractions and repulsions take place
under varied conditions. As the principle of this instrument and
the mode of observation is the same as in the case of the magnetic
balance, described in the preceding Book, we shall content ourselves
with simply stating the following laws.

The repulsion or attraction of two equal spheres charged with electri-
cities of the same or contrary kinds, varies in the inverse ratio of the
square of their distances. Af tractive or repulsive forces vary as the
products of the quantities of electricity which the two spheres contain.

This, it will be remembered, is the law which governs universal
gravitation.

The tension of electricity spread over the surface of a conducting
body is only equal at each point of the surface, when the body has the

542 PHYSICAL PHENOMENA. [BOOK vi.

form of a sphere. This is expressed by saying that the thickness of
the electric stratum is uniform (Fig. 355).

In an elongated ellipsoid, this stratum possesses its maximum
thickness at the extremities of the major axis ; in a flattened ellipsoid,
the maximum is round the equator. In a flat disc, the electric tension,
which is nearly nil at the centre, increases towards the edges, where

FIG. 355.— Tension of electricity at the different points of a sphere and of an ellipsoid.

it attains its greatest intensity. In a conductor formed like a cylinder
terminated by two hemispheres, the tension is greatest at the surface
of these latter ; and it is nearly nil everywhere else. The dotted lines
surrounding the solids represented in Figs. 355 and 356, indicate, by
their distances from the adjacent points of the surfaces, the tension
of the electricity at each of these points.

We see, therefore, what a great

(' WMMNMMMIIIDI^^ influence form has on the distri-

*-.^ \^/

bution of electricity on surfaces;
but nowhere is this influence so
perceptible as on the parts of
bodies terminated by abrupt edges,

Fl*. 356.-Ten,ion of electricity on a flat disc, aCUte angleS> and C0nical OT
and on a cylinder terminated by hemispheres. mi(M pointg< At these

electricity accumulates, and acquires sufficient intensity to pass into
the surrounding medium, even when this medium is only to a slight
extent a conductor. Before experimentally proving what is called the
power of points, we may say a word or two on the influence of the
medium which surrounds an electrified body, on the preservation or
loss of the electricity on its surface.

We already know that if this medium is a good conductor, such as
water or moist air, the electricity will not remain on the body which
has been electrified, but will pass away : this is an obstacle which
must be removed, however slight it may be, if we wish to acquire a
quantity of electricity. But if the medium is dry air, let us inquire

CHAP, i.] ELECTRICAL ATTRACTION AND REPULSION. 543

what will be the influence of atmospheric pressure on the loss of elec-
tricity from the surface of a body, and what the influence of tempera-
ture ? These questions are very complex, because the causes which act
at one time on the loss of which we speak, besides being numerous,
are very difficult to study separately. The insulating supports are more
or less conductors ; and the same remark applies to electrified bodies.
Coulomb and Matteucci studied this interesting and difficult question,
and did not always arrive at similar results. Nevertheless, their
researches have shown that the loss of electricity in dry air increases
with the temperature ; that with a constant temperature it increases
rapidly when the pressure of air diminishes, or rather as the air sur-
rounding the electrified body is rarefied. Nevertheless, this last law
only holds good in the case of strong charges ; so that, if we introduce
an electrified body into a vacuum, it immediately loses the greater
part of its tension ; but this action is limited, after which the loss
goes on very slowly. The greater the rarefaction, the less is the
limit, but the loss of electricity becomes less also. We shall
hereafter describe some very curious phenomena, which show the
loss of electricity in rarefied media.

We will now return to the escape of electricity at points.

It has been calculated that at the top of a conical point the
electric tension is infinite, so that it is impossible to charge a con-
ducting body, furnished with such a point, with electricity; this
is confirmed by experiment. In proportion as the electricity is
developed, it escapes into the surrounding medium and disappears.
When the extremity of the point is examined in the dark, a luminous
tuft is seen, the form and colour of which we shall hereafter study.
If, while the point is in communication with the electric source, the
hand is placed before or under it, a wind is felt which indicates
a continuous movement of the particles of air; this movement is
rendered very perceptible by placing at the end of the point the
flame of a candle (Fig. 357). The electric wind is intense enough
to cause the flame to bend, or even to extinguish it. This agitation
of the air, at the extremity of the points of electrified conductors,
was at first attributed to the escape of the electricity, which was
compared to a fluid ; but the following explanation appears to
us preferable, because it requires no hypothesis as to the nature of
electricity, and is, moreover, found to agree with known phenomena.

544

PHYSICAL PHENOMENA.

[BOOK vi.

The molecules of air, which are in contact with the point electrified
to a considerable degree of tension, are charged with electricity of
the same name as that of the conductor ; then commences repulsion,
and the molecules, on getting further away, give place to others, which

Fio. 357. — Power of points. Electric wind.

are electrified in their turn, and so on. Hence the current of air
which observation indicates, and which is only continuous so long
as the electric charge is renewed.

The force with which the air is driven
from a point, engenders a reaction, which
must repel the point in a contrary direc-
tion ; and if this point does not move, it
is because it is not free to do so. The
existence of this reaction is proved by using
a little instrument called the electric fly
(Fig. 358). A system of divergent wires
is united by a centre piece, which allows
the movement of the system in a horizontal
plane ; each wire is curved in and sharply
pointed in the same direction. As soon as
the conductor on which the fly is placed is charged, the latter takes up
a rotary movement in the direction opposite to that of the points.

Fio. 358.— Electric fly.

CHAP. II.]

ELECTRICAL MACHINES.

545

CHAPTEE II.

ELECTRICAL MACHINES.

Electrification at a distance ; development of electricity by induction — Distribution
of electricity on a body electrified by induction — Hypothesis as to the normal
condition of bodies ; neutral electricity proceeding from the combination of
positive and negative electricities — Electroscopes ; electric pendulum ; dial
and gold-leaf electroscopes — Electrical machines : Otto von Guericke's machine ;
Ramaden, or plate-glass machines ; machines of Nairne and Armstrong — The
electrophorus.

WHEN a body is in its normal condition, we have just seen
that there are two modes of rendering it electrical, viz. by
friction, or by contact with a body previously electrified. The
phenomena which we are about to describe prove that, in the latter
case, contact is not necessary. Let us take, for instance, an electrified

FIG. 359. — Electricity developed by influence or induction.

body c — a metallic sphere mounted on a glass column— and let us
place in its vicinity, at a short distance from it, an insulated cylin-
drical conductor A B, in its natural condition. These two bodies are no
sooner in the presence of each other, than the conductor A B shows

546 PHYSICAL PHENOMENA. [BOOK vi.

si<ms of electricity, as may be proved by bringing the pith ball of!
an electric pendulum near its extremities, when it is immediately
attracted by the conductor ; or still better by observing the small
pendulums a, 1}, fixed at different points of the cylinder, and formed
of pith balls suspended by conducting threads. These balls are
charged by contact with the same electricity as the parts which they
touch ; hence the repulsion which is shown by the deviation of the
pendulum threads from the vertical. This method of evoking
electricity, developed at a distance by an electrified body on a con-
ductor in its natural state, is called electrization by influence or
induction. Let us determine the nature of this electricity, and
the manner of its distribution on the conductor. If the sphere c is
charged with positive electricity, the extremity A of the cylinder,

FIG. 360. — Distribution of electricity on an insulated conductor electrified by induction.

nearest the sphere, is electrified negatively ; the extremity B is, on
the contrary, electrified positively. This can be seen, by presenting
successively to the two extremities a small insulated pendulum,
the ball of which is charged with a certain electricity ; for instance,
positive electricity. When held near A, it is attracted ; but when
near B, it is repelled. The reverse would take place if the sphere c
had been charged with negative electricity.

To study the distribution of these two opposite electricities on
the conducting cylinder, double pendulums with conducting wires
or threads are suspended at different distances, so that the divergence
of the balls can be observed. It will be seen that the electrical tension
is at a maximum at each extremity, and that it gradually diminishes
from each of these extreme points towards a mean position M, where it

CHAP, ii.] ELECTRICAL MACHINES. 547

disappears. The line of such points, as M, on the surface is called the
neutral line. The section of the cylinder which has remained in its
natural state is closer to the extremity nearest to the sphere than to
the other; it is not absolutely at the centre of the conductor electrified
by induction. We may also add that the electric tension is greater at
A than at B. Matters being thus arranged, let us gradually remove
the sphere. The balls of the pendulum will then be seen to gradually
approach each other, and to return to contact when the distance of the
sphere is sufficiently great. Ultimately all the influence ceases ; the
conducting cylinder returns to its natural state ; and it immediately
regains this state if, instead of removing the sphere, we discharge it
of its electricity by placing it in communication with the ground.

In the experiment just described, the conductor electrified by
induction was insulated. Let us suppose that after having placed it
in the presence of the inducing sphere — the charged body which elec-
trifies by influence being so named — the furthest extremity B were
made to communicate with the ground. Immediately all the elec-
tricity with which this part of the cylinder was charged would
disappear, and this latter would only contain the electricity opposite
to that of the sphere, but at a greater tension, as the more considerable
divergence of the pendulums proves. The maximum of tension would
be, as always at A, and the neutral line would have disappeared. The
nature of the remaining electricity, its distribution on the conductor,
and its tension at the different points would still be the same, if,
instead of touching it at B, every other part of the cylinder were made
to communicate with the ground, even the extremity A. Indeed, if
after having established this communication it is removed, all remains
in the same condition ; that is to say, the conductor is always charged
with electricity opposed to that of the inducing sphere, unequally dis-
tributed. On removing this sphere, the electricity remains on the
conductor ; but it is distributed equally over every part of its
surface, and we now have a body electrified by induction and charged
with electricity, as if it had been directly charged by friction, or
contact.

When we place in the presence of a source of electricity, such
as the sphere, not only one conductor, but a series placed in a row
A B, A' B', &c. (Fig. 361), they are all simultaneously electrified by
induction ; but the electric tension on each of the cylinders gradually

548 PHYSICAL PHENOMENA. [BOOK vi.

diminishes with the distance, although it is stronger on A' B', for
example, than it would be if the conductor A B were taken away,
and the induction was only exercised by the sphere alone. This
last observation proves that each conductor acts by induction, and
contributes to electrify that which follows it in the series.

The preceding facts are of great importance, and they have
suggested an hypothesis which, without theorizing as to the nature
of the first cause of electricity, gives a complete explanation of the
phenomena of attraction and repulsion, and electricity by contact, &c.
This hypothesis may be stated as follows : — A body in its natural
condition possesses simultaneously two kinds of electricity — positive
and negative— in such proportion that they neutralize each other,

FIG. 361.— Electrical induction through a series of conductors.

If it is rubbed with a second body, a separation of the two elec-
tricities is produced: one kind passes to one of the rubbed bodies,
and the other to the other, where they each find themselves in excess
when the bodies are removed, and they then manifest their presence
by the phenomena which we have described.

It is by this means that electrization by induction is explained ;
that is to say, the phenomena presented by the conducting cylinder
placed in the vicinity of the electrified sphere. The positive
electricity of this sphere attracts the negative electricity and
repels the positive electricity of the conductor; the first is at-
tracted towards the extremity A (Fig. 359), the second is repelled
towards the extremity B. But the attraction is stronger at A than
the repulsion at B, because the distance from the source is less at

CHAP, ii.] ELECTRICAL MACHINES. 549

the first region than at the second: this is the reason why the
neutral line D is nearer to A than B. When the conductor is placed
in communication with the ground, it is the same as if it had
been indefinitely lengthened, which explains the increase of tension
of the negative electricity at A ; the neutral line indefinitely removed
further back is no longer on the cylinder, so that if the communi-
cation is suddenly broken, negative electricity alone will be found
on it. This electricity is also found to be unequally distributed on
the surface, on account of the inequality of action of the sphere
on portions which are situated at increasing distances. The same
hypothesis will account for the first phenomena that we studied;
viz., the attraction and repulsion of light bodies by an electrified
body.

If the pith ball of an electrified pendulum is brought near a
glass rod c, charged with positive electricity, the neutral electricity
of the ball is decomposed by induction ; the positive is repelled to &,
if the thread is an insulating one, or sent back to the ground if it is
a conducting one ; the negative is attracted to a. In both instances,
the tendency of the positive electricity of the
ball and the negative electricty of the rod to
reunite, causes the pendulum to deviate from
the vertical : and attraction ensues. If there
is contact, the electricities combine, and

FIG. 362.— Cause of attraction

the ball remains charged with negative of light bodies,

electricity, always provided that it is insulated; hence, repulsion
between the two electricities of the same nature, which the two
bodies contain at this moment in the presence of each other. "When
the ball is not insulated, the positive electricity passes to the ground,
and contact determines the combination of the two contrary elec-
tricities; the ball then returns to its natural condition, and there
is no repulsion. These facts, as we have seen in the preceding
chapter, are proved by observation.

The electrization of an insulated conducting body by contact
of a body already electrified is also easily explained : before con-
tact the neutral electricity of the conductor is decomposed by
induction ; there is attraction of the positive electricity — let us
say, of the body previously electrified — to the negative electricity
of the conductor, and repulsion of the positive electricity. Contact

550 PHYSICAL PHENOMENA. [BOOK vi.

determines the combination, in a certain proportion, of the electri-
cities which attract each other, and there remains on the conductor
an excess of positive electricity ; hence there is a charge of electricity
of the same nature as that of the electrical source, which at first
caused it to be believed that electrization was caused by a flow of
electricity somewhat similar to that of a fluid : and the hypothesis
appeared the more true as contact diminished the electric charge
of the source. In reality there is no division of electricity between
the two bodies ; but rather an action of decomposition by induction,
than a partial combination. This combination often takes place
through the air a little before contact, and it is, as we have seen,
accompaned by a slight explosion and a spark.

Lastly, the action of points also finds a more complete explanation
on the preceding hypothesis than on that which we vaguely indicated
above. When a conductor terminated by a point is presented to an
electrified body, the neutral electricity of this conductor is decom-
posed by induction; and as the electricity opposed to that of the
electrified body possesses at the extremity of the point an infinite
tension, it effects a rapid combination with the two electricities of
contrary names, and the electrified body is found to be discharged.

These rather dry preliminaries are indispensable to the compre-
hension of the phenomena which we have to describe ; indeed,
without them, it would be impossible to understand the functions
of electrical machines, or the numerous experiments which they
enable us to make.

Before commencing a description of these we may say a few
words on the apparatus termed electroscopes, because they are em-
ployed to prove the presence of free electricity developed on a
body, and to measure its tension.

The electric pendulum, which we have already described, is an
electroscope, and we have pointed out many of its uses.

The dial electroscope or quadrant electrometer is represented in
Fig. 363. It is formed of a conducting support, surmounted by an
ivory scale; at the centre of the scale is suspended the rod of a
pendulum with a pith ball ; the rod is very thin and is also of ivory.
When this apparatus is placed on a body charged with electricity,
the latter pervades all parts of the electroscope. The pith ball, at

CHAP. IT.]

ELECTRICAL MACHINES.

551

FIG. 363.— Quadrant electroscope.

first in contact with the support, is repelled, and its deviation from
the vertical is indicated by the divisions of the scale, the angle being
greater as the electrical charge of the body is greater.

The gold-leaf electroscope (Fig. 364) is composed of a glass bell-jar
placed on a metal plate, to the interior of which passes a brass rod
surmounted on the outside with a ball.
This metallic rod supports two gold
leaves which remain vertically in con-
tact, when the electric charge of the
apparatus is nil, and which diverge
under contrary conditions. The fol-
lowing is the mode of using gold-leaf
electroscopes when we desire to know
whether a body is electrified or the

reverse. The body in question is slowly brought near to the outer
ball ; if it is not charged with electricity, the leaves remain in
contact : if on the contrary it is electrified, positively, for instance,
the neutral electricity of the system formed by the ball, the metallic
rod, and the gold leaves, will be decomposed by induction, the
negative electricity attracted into the ball, and the positive electricity
repelled into the gold leaves ; these will then diverge, forming an
angle between them varying with the
electrical charge of the body. If we
now touch the ball with the finger, the
electricity of the same nature as that
of the inducing body will escape to
the ground; a fact which we have
before proved in describing the phe-
nomena of electrization by induction.
The gold leaves will then approach
each other, and the system will be
charged with negative electricity, prin-
cipally accumulated in the ball. If
the finger and the inducing body are
simultaneously taken away, this same FIG. 364.— Goid-ieaf electroscope,
negative electricity will be extended through the system and will
cause the gold leaves to diverge again.

The electroscope is, by this operation, charged with electricity

552 PHYSICAL PHENOMENA. [BOOK vi.

which is always of a contrary nature to that of the body which has
been presented to it. It is useful to learn how to distinguish the
nature of this electricity when it is unknown. This is effected by the
following means : a body charged with a known electricity is placed
near the ball of the instrument, for instance a stick of resin electrified
negatively ; in the case we have supposed, that is to say, when the
leaves are charged negatively, the influence of the negative electricity
of the stick will manifest itself by an increased divergence of the
gold leaves, the negative electricity of the rod being repelled into these,
and the tension will thus be augmented.

If, instead of a stick of resin, a glass rod positively electrified, were
used, the contrary electricities of the gold leaf and the glass would be
attracted ; the divergence, instead of increasing, would be diminished
until contact ensues. But in this case there might be a cause of error,
because after the gold leaves have come in contact, the influence of
the glass rod may determine a fresh decomposition, and hence a diver-
gence. It is better, therefore, when there is not divergence at first, to
make a second trial with a body charged with the contrary electricity.

Such are the proofs by the aid of which the nature of the elec-
tricity of a body can be determined when this body has been employed
to charge the electroscope. It is evident that we might pursue a
different course by charging the electroscope with a known electricity,
and then using it to discover the kind of electricity which a body
possesses.

ELECTRICAL MACHINES.

We already know that, by the aid of a body electrified by friction,
it is possible to electrify another by induction. It is now time to
describe the principal machines which have been invented for collect-
ing positive or negative electricity; the construction of which is
based, as we shall see, on these two modes of electrization.

The invention of the first electrical machine is due to Otto von
Guericke ; it consisted of a globe of sulphur or resin mounted on an
axis, to which a rapid rotatory motion could be communicated. "When
the hands were pressed against this globe, the resulting friction
rendered the non-conducting body electrical ; and in order to collect
the electricity thus developed, a metallic cylinder was suspended
horizontally above the globe by silken cords. One of the extremities

u u

CHAP, n.j ELECTRICAL MACHINES. 557

of this cylinder was on a level with the globe of sulphur, or some-
times a metal chain descended from the conductor to a short distance
from the surface of the globe. The electricity developed on the sur-
face of the sulphur decomposed by induction the neutral electricity
of the insulated conductor, which was thus charged at its extremities
with opposed electricities. Fig. 365 represents an electrical machine
of this kind as it was constructed in the eighteenth century, by the
aid of which the Abbe Nollet performed a number of amusing and
curious experiments in public.

The plate-glass electrical machine is the most generally used of all
modern apparatus of this kind. Fig. 366 will render its construction
intelligible. A large circular glass plate is mounted vertically on a
metal axis, which can be turned by means of a handle ; as it passes
between the two wooden stands which support the axis of the plate,
the surface of the glass rubs against two systems of cushions fixed to
the stands. The rotatory movement thus produces electrization of the
glass plate, which is charged with positive electricity on both sides.
The cushions are not insulated, in order that the negative electricity
with which they are charged may escape : if this electricity continued
to accumulate on the cushions, a time would arrive when its influence
on the positive electricity of the plate being equal to that due to the
friction, would necessarily limit the charge ; a metallic chain therefore
puts the stands and cushions in communication with the ground.

The cushions are stuffed with horsehair, and covered with leather,
the surface of which is covered over with aurum musivum, or an
amalgam of zinc ; experiment has proved that these latter substances
facilitate the production of electricity.

Such is the arrangement of that part of the machine which
produces the electricity ; the conductors are charged in the manner
now to be described. There are two long brass cylinders, with sphe-
rical ends, insulated on glass legs, the cylinders being united by a
small transversal cylinder. The two extremities of these cylinders near
the glass have metallic prongs, furnished with points, turned towards
the glass plate, but at a sufficient distance to prevent contact during
the rotatory movement. When the glass plate becomes charged, the
positive electricity acts by induction on the neutral electricity of the
conductor, decomposes it, and attracts the contrary electricity, — that

558

PHYSICAL PHENOMENA.

[BOOK vi.

is to say, the negative, which escapes by the points, by neutralizing
equivalent quantities of the positive electricity of the glass. The
positive electricity of the conductor is, on the contrary, repelled to
the two metallic cylinders, where it accumulates. On one of these
is placed a quadrant electroscope, furnished with a pendulum which
shows the tension of the collected electricity. The glass is electrified
in proportion as it rubs against the cushions, but the electricity
disappears from it on passing before the points of the prongs. There
are then only two sectors of the circle which are electrified ; those
which are seen in the figure protected by screens of oiled silk, which
prevent loss through the humidity of the air. In order to cause the
machine to work well, the air of the room must be dry and at a
sufficiently high temperature ; and before an experiment, the glass
supports, which insulate the conductors, must be carefully wiped.

Fio. 367.— Nairne's machine, furnishing the two electricities.

Eamsden, an English instrument-maker of the eighteenth century,
was the inventor of the plate machine, the construction of which has
been perfected since that time.

By means of Nairne's machine (Fig. 367) positive and negative
electricity can be obtained at the same time, but on two separate

CHAP, ii.] ELECTRICAL MACHINES. 559

conductors. One of the conductors is furnished with points; it is
electrified positively like those of the plate machine ; the other
conductor has a cushion, the friction of which against a glass
cylinder determines the separation of the two electricities which
form the neutral electricity of the system : a piece of silk also
protects the surface of the glass from loss of developed electricity.
Hence it follows that, whilst positive electricity accumulates on the
glass, the negative is repelled to the cushion, and thence to the
conductor. Only one of the two electricities can be collected : for
this purpose, the conductor which contains the other electricity must
be made to communicate with the ground, by means of a chain.

Van Marum invented an electrical machine which could be worked
either like that of Eamsden, or that of Nairne ; either positive or
negative electricity could be collected on its conductors, or both at
the same time.

If very dry mercury is shaken in a glass tube — in a barometer
tube, for instance — -we see in the dark, a very faint light, which
proves the production of a certain quantity of electricity ; and, indeed,
the glass tube then attracts light bodies. Friction of liquids against
solids may also be employed as a method of electrization. But for-
merly we did not know how to utilize this action ; a method, however,
was discovered by chance in 1 840, when a very efficient means of ob-
taining electricity by the friction of a jet of vapour mixed with minute
liquid spherules, against a solid, was devised. Such is the principle
of Armstrong's hydro-electrical machine, represented in Fig. 368.

A boiler, insulated by glass supports and filled with distilled
water, is used to produce high- pressure steam ; this escapes into
the air through a series of jets, after being partly condensed in
its passage through a box of water filled with wet packing, kept
constantly moist.

The liquid drops, produced by the condensation of the vapour,
rub with force against a layer of boxwood, which surrounds them,
before penetrating into the jets by which they escape, and also
against the sides of the jets, formed of the same wood. Electricity
is thus developed in greater abundance as the pressure of the steam
is higher: the boiler becomes charged with positive electricity,
and the vapour with negative. To collect the latter, an insulated

5GO

PHYSICAL PHENOMENA.

[BOOK VI.

conductor, furnished with a series of points, is placed before the jets
of vapour.

Hydro-electrical machines possess great power, and it is to be
wished that they were more used. Among machines of this kind,
that of the London Polytechnic Institution is said to be furnished

FIG. 368. — Armstrong's hydro-electric machine.

with forty-six vapour jets, and to give sparks twenty-four inches in
length ; that of the Sorbonne, in Paris, has eighty jets, and also
furnishes continuous sparks of several decimetres in length.

We often employ in physical and chemical laboratories a more
simple apparatus than that we have just described, which is com-

CHAP. II.]

ELECTRICAL MACHINES.

561

petent to produce electricity rapidly ; we allude to the electrophorus.
It is composed of a disc of resin, sulphur, or caoutchouc, for instance,
melted into a mould of wood or brass, and of a metal plate with rounded
edges, furnished with an insulating handle. The resin, sulphur, or
caoutchouc is electrified by rubbing it obliquely with a cat's skin ; —
it is thus charged with negative electricity ; the metal plate is then
placed on the electrified cake, and the neutral electricity of the metal
is decomposed by induction, so that the lower surface in contact with

FIG. 369. — Electrophorus with resin cake.

the resin is electrified positively, and the upper surface negatively.
On touching the upper surface with the finger, its negative elec-
tricity escapes to the earth ; and if the metallic plate is then raised
by the insulating handle, it remains charged with positive electricity
in sufficient quantity to produce a spark.

We must remark that the electricity collected is not produced by
the contact of the resin with the metal, — a contact which only takes

X X

562 PHYSICAL PHENOMENA. [BOOK vi.

place in a few points of the surface. The cake of resin remains
after the experiment, charged with negative electricity, so that the
experiment can be repeated successfully several times and at long
intervals. An electrophorus, placed where the air is very dry,
preserves for whole months the electricity developed on its surface
by friction.

Very curious lecture experiments can be made with the machines
just described, which have been constructed in various forms. In
mentioning some of the more interesting, we shall have occasion to
study, in the most complete manner, the various effects of the
mysterious agent whose existence, two centuries ago, was scarcely
recognised ; and we shall, moreover, be able to familiarize ourselves,

with explanations of the general pheno-
mena which have formed the subject of
the preceding chapters.

A metallic rod is suspended to one of
the conductors of an electrical machine,
and three bells are suspended from the
rod, the two end ones by brass chains, that
in the middle by a silk thread ; this com-
municates with the ground by' a metal
chain. Lastly, between the bells, two little
metallic balls (Fig. 370) are suspended by

FIG. 370.-Electrical bells. ^ threads

As soon as the 'machine is worked, the electricity of the conductor
passes to the end bells, and the insulated balls are attracted, then
repelled, so soon as they have established contact ; the middle bell,
which is in its natural or neutral state, when it is subjected to the in-
duction of the two outside electrified bells, is charged with electricity
of a contrary nature to that of the balls, and attracts them until they
come in contact, and, in its turn, repels them. Then follows a series
of successive blows and sounds, which are repeated as the conductor
of the machine is charged. From this the name of electrical bells is
given to this apparatus. Fig. 371 represents an apparatus invented
by Volta for the purpose of explaining the movement of hailstones
during storms ; a glass bell-jar communicates with the ground by the
plate on which it rests ; a metallic rod, in contact by its outer extremity
with the conductor of an electrical machine, passes into the bell-jar, and

CHAP. II.]

ELECTRICAL MACHINES.

563

the other extremity is furnished with a metal plate. On the bottom
of the bell-jar a number of pith balls are placed. As soon as the
machine is charged, the eleotricity passes to the plate, attracts the
balls, which are electrified by induction and come into contact with
the plate ; they are then repelled, and fall to the bottom of the jar,
where they discharge their electricity and return to their neutral state.
These backward and forward movements continue so long as the
conductor is charged with electricity ; the phenomenon is known under
the name of electrical hail. Sometimes the pith balls are replaced
by little figures made of the same
material, and this is called the
puppet dance.

These three experiments prove,
as we see, in an amusing form, the
phenomena of electrical attraction
and repulsion. We will now study
the effects of electrical discharge
between conducting bodies.

We have seen that if when an
insulating body, a glass rod for
instance, is electrified, we bring
the finger near its surface, a spark,
accompanied by a crackling sound,
passes, while the glass remains
electrified at its untouched por-
tions ; which is explained by the
non-con due tibility of the body em-
ployed. If, instead of an insulating

body, a conductor is substituted, such as that of a charged electrical
machine, the effect produced is much more energetic and the discharge
more complete ; moreover, the phenomena then observed depend on
the manner in which the discharge is made, — that is to say, on the
nature of the medium interposed between the electrified conductor
and the body submitted to its influence.

If the finger or any other part of the body is brought near the con-
ductor of the machine, a spark is produced, and the sensation is stronger
as the charge is greater. The quadrant electroscope placed on the con-
ductor then falls to zero, showing that the electricity has been discharged;

x x 2

FIG. 371.— Electrical hail.

564 PHYSICAL PHENOMENA. [BOOK vi.

but when the plate is turned in a continuous manner the sparks succeed
each other with rapidity ; the noise is a kind of crackling, and we feel
a pricking sensation without any sharp shock. If the hand is not very
near the conductor, the tension of the two electricities, as much that
of the machine as that developed in the body by induction, becomes
very strong; and when it is sufficient to overcome the resistance
opposed by the distance to their recomposition, a long spark passes,
and the shock shakes the whole arm. If, before turning the plate of
the machine, a person is placed on an insulating stool,
that is, a stool with glass supports, and he then places
his hand on the conductor, he will be electrified at
the same time as the latter; his body is then virtually
a part of the conductor. Another person, not insu-
lated, will be then able to draw sparks from his body,
and each one will thus receive, at the same time, the
shock which the discharge produces.

The luminous effects which the disengagement of
electricity produces deserve a special and detailed
study. We shall return to this hereafter, when we
have reviewed the various methods of producing
electricity; but we may now describe some experi-
ments in which the production of the spark gives rise
to singular actions of light. i

On the surface of a glass tube a number of little
lozenges of tinfoil are pasted in a spiral curve, a
small space being always left between each of them.
The extremities of the spiral and of the tube are two
metallic rings, one connected with the conductor of
the electrical machine, whilst the other communicates

FIG 372— LUDUIOUS w^ ^e g1"0111^ by a chain (omitted in the figure).
tube. £s goon ag ^-ne machine js charged, decomposition of

the neutral electricity of the first tinfoil lozenge takes place by
induction, then of the second by the first, and so on through the
whole series. The small distance causes simultaneous discharges,
and sparks appear at the same time along the entire spiral ; the
phenomenon lasts so long as the plate of the machine is turned
(Fig. 372). This is the experiment of the luminous tube.

Similar luminous effects are obtained by means of a glass globe

CHAP. II.]

ELECTRICAL MACHINES.

565

on the surface of which small tin lozenges are pasted so as to produce
various designs. This is the luminous globe (Fig. 373). If on a,
rectangular sheet of glass, bands of tinfoil are pasted so as to form an
uninterruped series of parallel lines as in Fig. 374, a pattern of any
form may be cut on this ground with a sharp point. A spark will
appear at each solution of continuity when the extremities of the
series are placed, the one in communication with the conductor of
the machine, and the other with the ground ; the figure drawn on the
glass will be seen in the form of luminous lines. This is the luminous

FIG. 373. — Luminous globe.

FIG. 374.— Luminous square.

square. The magic pane only differs from the preceding by the
irregular arrangement of the pieces of metal between which the
electric spark appears : metallic filings are carelessly thrown on the
surface of the glass covered with gum ; when the pane is connected
on one side with the machine, and the other with the ground, sparks
appear, and trace out irregular and serpentine lines, their positions
and figures changing every moment.

In the experiments just described, the discharge takes place
between two bodies charged with contrary electricities, separated from

566

PHYSICAL PHENOMENA.

[BOOK vi.

each other by an insulating medium, such as the air or glass. This
recomposition of the two electricities is called a disruptive discharge,
"because it is accompanied by a violent movement of the molecules of
the insulating body, which is proved by the following experiment : —
Two communicating tubes, of unequal diameter, the larger closed
the smaller open at the top, contain a certain quantity of water
(Fig. 375). In the large tube, two metallic rods, terminated by balls,
are fixed, one to the base, the other to the upper part, and they com-
municate respectively with the ground and with the conductor of
the electrical machine. As soon as the spark appears, the water rises
quickly in the open tube, then immediately regains its level. This
shock is produced by the violent disturbance of the molecules of the
air, and not by an expansion due to an elevation of temperature of
the whole gaseous mass, as was at first believed by Kinnersley, the
inventor of the apparatus. Nevertheless, it is still called Kinnersley 's
thermometer.

PIG. 375. — Kinnersley's thermometer.

FTG. 376.— Electrical mortar.

The sudden expansion of which we have just spoken led to the
invention of the electric mortar (Fig. 376), the action of which is
easily understood ; when the spark passes, the ball is projected to
some distance.

For the present, we will confine ourselves to these few experi-
ments. Those of our readers who possess apparatus may easily
repeat them.

CHAP, in.] LEYDEN JAR, 567

CHAPTEE III.

LEYDEN JAR. — ELECTRICAL CONDENSERS.

The experiments of Cuneus and Muschenbroeck ; discovery of the Leyden jar —
Theory of electrical condensation ; the condenser of jEpinus-— Jar with movable
coatings— Instantaneous and successive discharges — Leichtenberg's figures —
Electric batteries — The universal discharger — Apparatus for piercing a card
and glass — Transport and volatilization of metals ; portrait of Franklin —
Chemical effects of the discharge ; Volta's pistol — Fulminating pane.

/H UNEUS, a pupil of Muschenbroeck, a celebrated physicist of the
vJ last century, endeavoured one day to electrify water contained in
a wide-necked bottle. To effect this, he held the bottle in one hand,
after having passed a metal rod suspended on the conductor of an
electrical machine into the liquid. When he imagined that the water
was sufficiently charged with electricity, he lifted up the iron wire in
contact with the conductor with one hand, without removing the
other from the bottle, and he immediately felt a violent shock which
filled him with surprise. Muschenbroeck repeated the experiment of
Cuneus, but the shock which he received caused him such fear that
on communicating this fact (which was unknown among electrical
phenomena at that time) to Keaumur, he told him that no inducement,
not even the offer of the crown of France, would induce him to receive
another shock. Other physicists, however, were less timid. Allaman,
Lemonnier, Winckler, and the Abbe* Nollet, varied the experiment in
many ways, and science was enriched with a new electrical instru-
ment— the Leyden jar, thus named from the place where the experi-
ment was first made, in 1746. The following is the way in which
this apparatus is now constructed : —

A bottle made of thin glass has its bottom and three-quarters of
its height covered with a metallic coating, generally of tinfoil ; this is

568

PHYSICAL PHENOMENA.

[BOOK vi.

called the outer coating or armature of the jar. The interior coating
or armature is sometimes a metal lining the inside of the jar. Some-
times the bottle is filled with a quantity of gold leaves or tinsel : in
Muschenbroeck's jar, water was the conducting body. Lastly, a brass
rod, with a hook at one end, terminated above by a little ball, is
passed through the cork which closes the neck, and communicates
with the inner coating of the bottle.

To charge the Leyden jar it is suspended by its rod to the
conductor of an electrical machine, care being taken to establish, by

FIG. 377. — Cuneus' experiment (the Leyden jar).

means of a metal chain, communication between the ground and the
outer coating. It can also be held in the hand by the latter, and
then presented to the conductor of the machine.

When the bottle is charged with electricity, if the outer and inner
coatings are connected by a conducting body, a discharge takes place
accompanied by a spark and explosion. If the apparatus is held in
one hand and the other is placed near the ball, the discharge will pass
through the arms and body, and we receive the shock which frightened
the first operators so much. If several persons hold each other by
the hand, two and two, the first of the series holding the bottle and

CHAP. III.]

LEYDEN JAR

569

presenting the rod to the last one, as soon as contact is made, the
shock will be felt at the same time by all. Nollet showed this ex-
periment before Louis XV. ; three hundred French guards formed
the chain and simultaneously received the shock produced by the
instantaneous discharge of the Leyden jar.

Before describing the many curious experiments which may be
made with this apparatus, we will endeavour to give the theoretical
explanation of the double phenomena of the charge and discharge c f
the Leyden jar. We may first observe that
the apparatus must be composed of two
conducting bodies, the exterior and interior
metallic coatings, and of an insulating
body, which separates them — the glass
bottle. When the hook is suspended on
the electrified conductor of a machine, the
electricity of the latter passes to the surface
of the inner coating, which is thus charged
with, say, positive electricity. This elec-
tricity decomposes the neutral electricity of
the outer coating by induction, attracts the
negative electricity to the surface of the
glass, and repels the positive electricity to
the ground, through the medium of the
body of the operator or through the metal-
lic chain. Thus two charges of contrary
electricities are brought together, which
the interposition of the insulating glass
prevents from combining. If the union
of these two electricities is desired, we
unite them by any conductor whatsoever, and their combination is
accompanied by explosion and a spark. Hitherto it has not appeared
necessary to adopt any other explanation : the preceding rationale
also accounts for the phenomena of electrical induction, but we shall
see that it is, in reality, insufficient.

First, the size of the spark and the violence of the shocks indicate
in this case an electrical tension of an unusual energy ; the accumula-
tion of the two electricities in such quantity no longer seems in pro-
portion to the small dimensions of the conductors which compose the

FIG. 378.— Charging the Leydea jar.

570

PHYSICAL PHENOMENA.

[BOOK vi.

apparatus. The following is a fact which also requires explanation : —
When a Ley den jar is discharged and it is placed aside for a while, it
will be found somewhat charged without having been again placed in
communication with the source of electricity. A second spark will
appear, but weaker than the first. This is called a secondary discharge.
It is evident, therefore, that the Leyden jar accumulates a larger
quantity of electricity than that which can be obtained by the use of
simple insulated conductors. For this reason it is named, in common
with all similar apparatus, a condenser. Let us now inquire whence

FIG. 379. — The condenser of ^Epinus.

comes this power of accumulation, and what new phenomena inter-
vene to produce it. The theory of electrical condensation, first
propounded by ^Epinus, will enable us to understand this and the
cause of the preceding phenomena.

The condenser invented by this physicist is represented in Fig. 379 ;
it consists of two insulated metallic plates A., B, mounted opposite each
other on glass supports, and separated by a glass disc. They move in
a groove, and can thus be brought as near together as may be desired,
or, at least, with only the thickness of the insulating disc between
them. Quadrant electroscopes are fixed on the metallic rods which
support the two plates.

CHAP. III.J

ELECTRICAL CONDENSERS.

571

Let us suppose that the plates are at first some distance from each
other, and let A be put in communication with the electrical machine.
It becomes charged with positive electricity, the tension ending by
being equal to that of the source, and its electroscope diverges.
Moreover, this tension is nearly equally distributed over the two sides
of the plate A (Fig. 379). Let us now approximate the plates A and B ;
the latter will be charged by induction with negative electricity on
the side facing the glass disc, and positive electricity on the other
side, and its electroscope will also diverge ; but if the communication
of A with the electrical machine is discontinued, the attraction of
the negative electricity of B for the positive electricity of A goes on
increasing on the anterior side of the plate, and the electroscope of A

FIG. 380. — Charging the condenser of ^Epinus.

will again fall to zero. If B is now put in communication with the
ground, the positive fluid escapes, a fresh decomposition is made, and
the negative electricity is accumulated on the anterior side of this
plate, in greater quantity than before ; and by reaction, the tension on
the plate A has become stronger on the anterior side to the detriment
of the posterior face, which returns to its normal condition. Again,
when the communication of A is re-established with the electrical
machine, a fresh quantity of positive electricity passes to A, and the
condensation will still increase (Fig. 380). The same series of opera-
tions continued from time to time will produce a maximum conden-
sation on one or other of the plates. It will be now easily seen that
the condenser of ^Epinus and the Ley den jar only differ in form, and

572

PHYSICAL PHENOMENA.

[BOOK vi.

that the phenomena which can be observed in the one take place in
the same manner in the other. Let us inquire next what part the
glass disc plays in the experiment. Both theory aiid experiments
prove that a layer of any other insulating substance, for instance a
layer of air interposed between the conductors, gives rise to the same
phenomena; but as the air presents a more feeble resistance than the
glass to the opposite tensions of the contrary electricities accumulated
on the sides opposite the conductors, only a feeble condensation would
be obtained. Hence the necessity of interposing a more resisting
body, like glass or resin.

Moreover, according to the numerous experiments of Faraday
and Matteucci, it has been proved that the
two charges, positive and negative, are not only
accumulated on the surfaces in contact with
the glass and with the coatings of the con-
densers, but that the electricities actually pene-
trate the glass so a certain depth. This fact
has been proved by means of a Ley den jar,
with movable coatings formed of three parts,
as represented in Fig. 381. After charging
the whole jar, it is placed on an insulator, the
inner coating is raised by means of a glass hook,
then the glass jar, and it will be noticed that
there is very little electricity on the coatings,
whilst the jar itself is strongly electrified. More-
over, after having discharged the two coatings, if
they are again replaced the jar produces a spark
as bright as if the partial discharges had not taken place. The
penetration of the electricity to a certain depth into the insulating
body of the condensers explains, in a satisfactory manner, the
secondary discharges of the Leyden jar ; it shows, moreover, that the
metallic coatings also perform the part of placing the different parts
of the glass in easy communication, and in virtue of their conducti-
bility, the discharge is made instantaneously, and with its whole force.
We will now describe some curious experiments which may be
easily made with this condenser.

The discharge of the Leyden jar can be made instantaneously or
gradually, without the danger of any shock to the operator.

FIG. 381.— Leyden jar with
movable coatings.

CHAP. III.J

ELECTRICAL CONDENSERS.

573

The instantaneous discharge is made by means of a discharger :
this consists of two metallic rods, turning on a common joint, and
furnished with glass handles (Kg. 382). The handles are taken
in the hands, and the two metal balls which are at the ends of the
rods are placed, one near the ball of the inner coating, and the other
touching the outer coating of the Leyden jar ; the discharge is made
through the branches of the discharger. Successive discharges are
sometimes made with the bell Leyden jar, shown in Fig. 383.
The insulated pendulum which surmounts a bell fixed on a metallic
sland, and communicating with the exterior coating, is successively

FIG. 382. — Instantaneous discharge of a Leyden jar by means of the diseluiryer.

attracted and then repelled by the electricity of the interior coating,
afterwards to undergo the same actions from the other bell. At
each contact, the ball takes away a part of its electricity, alter-
nately from the one and from the other of the two coatings. The jar
is thus gradually discharged. Sometimes the ball of the pendulum
is made in the form of a spider, with legs made of pieces of silk.

Experiments with the sparkling jar (Fig. 384) prove that, in the
instantaneous discharge, the electricity comes from all parts of the
glass to converge towards the point where the reunion of the accumu-
lated electricities on the two coatings takes place. The exterior coat-

574

PHYSICAL PHENOMENA.

[BOOK vi.

ing is formed, as in the magic square, of fragments of metal filings, or
tinsel, fixed on a layer of gum ; and a band of metal which comes out at
a little distance from the outer coating is fixed to the interior coating.
When the jar is sufficiently charged, lines of fire will be seen to wind
about its surface, starting from the point where the discharge begins
(Fig. 384). We have just seen that the Ley den jar is charged with
contrary electricities on the two sides of the coatings ; a German
physicist, Leichtenberg, devised a very interesting experiment to

FIG. 383.— Successive discharges of a Leyden jar.
Chimes.

FIG. 384.— Sparkling Leyden jar.

prove this. He took a cake of resin, similar to that of the electro-
phorus, then charged a Leyden jar, and traced on the cake with the
ball some figure, the letter G for example ; he then replaced the jar,
and taking hold of it again, this time by the hook, he traced another
design on the cake with the lower edge of the jar. He next pro-
jected a cloud on the surface of the cake by means of bellows filled
with a powder formed of minium and sulphur ; the minium was
seen to place itself on the parts touched by the ball, — that is to

CHAP. III.]

ELECTRICAL CONDENSERS.

575

say, negatively electrified, whilst the sulphur attached itself to the
parts charged with positive electricity. Figs. 385, 386, and 387 are
fac-similes of Leichtenberg's figures, which M. Saint Edme, Demon-
strator of the Physical Lectures at the Conservatoire des Arts et
Metiers, has kindly prepared for this work. The two drawings,
positive and negative, obtained by the contact of the resin with the

FIG. 385.— Leichtenberg's figures. Distribution of the two kinds of electricity.

two coatings, are distinguished not only by the colour of the powders
which cover them, but also by the form of the singular ramifications
which the contrary electricities have traced on the resin.

To obtain stronger effects we must increase the size of the
Leyden jar.

576

PHYSICAL PHENOMENA.

[BOOK vi.

The glass jar, with a large aperture, which allows tiufoil similar
to the outer coating to be pasted within it, is called an electrical jar.
Several jars placed together, as shown in Fig. 388, form a battery.
All the interior coatings are then connected together by means of
metallic rods, proceeding from the ball of each of them, and radiating
towards the largest ball of the centre jar ; the latter ball is put in
communication with the conductor of the electrical machine, when
the battery is to be charged. The outer coatings are connected
together by contact with the tinfoil, with which the inside of the

FIG. 386. — Leichtenberg's figures. Distribution of the positive electricity.

box is covered, and which communicates with the ground by a
metallic chain.

The electric charge which these powerful condensers accumulate
on their coatings is very considerable, and some time is required to
furnish them, by ordinary machines, with the electricity they are
capable of condensing. The operation can be made more rapid by
dividing one battery into several batteries, each inclosing two or
three jars, and causing them to communicate, two and two, by rods

CHAP. III.]

ELECTRICAL CONDENSERS.

577

uniting the interior coatings. The discharges of electrical batteries
obviously become more dangerous as the jars increase in surface and
number. A battery of six elements of medium size would give very
stron g shocks, sufficient indeed to kill such animals as rabbits and
dogs. Precautions must be taken when they are discharged ; for this
purpose the universal discharyer (Fig. 389) is used, as well as for
numerous other experiments. This apparatus is formed of two brass
rods, each terminated at the one end by a ring, to which a chain can be
attached, and at the other by a knob. The rods are insulated on glass

FIG. 387. — Leichtenberg's figures. Distribution of the negative electricity.

supports, and are movable on a joint. The knobs are directed towards
a stand, on which the body through which the discharge is to be
passed is placed. One of the chains communicates with .the ground,
and the other with an ordinary discharger, by which the central
knob of the electrical battery can be touched without danger.

We will conclude this chapter with the description of some ex-
periments which show the different mechanical and physical effects ol
electricity accumulated in condensers.

Y Y

578

PHYSICAL PHENOMENA.

[BOOK vi.

In the experiments of the electric niortar and Kinnersley's ther-
mometer, we have already seen the mechanical effects which the
disruptive discharge can produce. The violent displacement of the
molecules of the body interposed between the two conductors is
rendered still more manifest in the apparatus for perforating a card,
or a sheet of glass.

A card is placed between two points with metallic conductors
separated by a glass rod (Fig. 390). A charged Leyden jar is then
held in the hand, having its exterior coating in communication with

FIG. 388.— Battery of electrical jars.

one of the conductors by a metallic chain ; the knob of the inner
coating is now brought near the other conductor. The discharge takes
place through the card, which is found to be pierced with a hole be-
tween the two points. We do not know why the hole is nearer the
negative point than the positive, in the open air, whilst this is not the
case when the experiment is made in vacuo ; but such is the case.

A piece of glass of 1 or 2 millimetres in thickness can be pierced
in the same manner, by placing it horizontally between the two

CHAP, in.] ELECTRICAL CONDENSERS. 579

points (Fig. 391) ; care must be taken, however, to cover each of the
metallic points with oil, to prevent the electricity from being diffused
over the surface of the glass. After the discharge, a small round hole
is found in the glass ; and the glass in its path has been pulverized
by the passage of the electricity. In order to make this experiment
succeed it is necessary to use a powerful battery, but even when the
discharge is not strong enough to pierce the glass it is found to be
altered and rough at the point where the spark appeared.

FIG. 389. — Universal discharger.

The calorific effects of the electrical discharge are not less
interesting than the mechanical effects. If the two balls of the
universal discharger are united by a very fine metallic wire, of
silver for example, the wire becomes incandescent, and it is
melted and vaporized if the electrical charge is sufficiently strong.
With the powerful batteries of the Conservatoire des Arts et
Metiers, iron wires several yards in length can be melted. Wires

y y 2

580

PHYSICAL PHENOMENA.

[BOOK vi.

of the same diameter and the same length require very difi'erent
electrical charges to melt them : iron, lead, and platinum melt more
easily than gold, silver, and especially copper. Fusion is caused
more readily if the discharge takes place in air, than if it is made
in vacua. If a gilded silk thread is placed between the balls of the
universal discharger, the discharge melts the gold and leaves the silk
intact ; and the particles of the volatilized metal can be collected on
a white card, on which the thread may be placed before the experi-
ment. A blackish spot will be seen on the card, formed of very fine
volatilized powder of gold. By working with different metals, spots

FIG. 390.— Experiment of perforating a card.

of various colours can be obtained, and, if the metals used are
oxidizable at very high temperatures, the markings obtained are
formed of metallic oxides, reduced to impalpable powder. In the
last century, Van Marum made some very beautiful experiments on
the transport of metals by the electrical discharge. Fusinieri, having
passed a discharge between two balls, one of gold and the other of
silver, observed that the first was silvered and the second gilded
round the points between which the spark appeared. It is probable
that the phenomena of which we have just spoken are complex,
and are due, at the same time, to the rise of the temperature

CHAP. III.]

ELECTRICAL CONDENSERS.

581

produced by the discharge, and to the mechanical transport of the
molecules.

This property has been made of use to obtain metallic prints
reproducing various drawings. In lectures, the experiment of Frank-
lin's portrait is sometimes made. Fig. 392 shows a thick sheet of
paper in which the portrait of the illustrious physicist is cut ;
layers of tin are pasted on each side of the sheet, which is also
covered above with gold leaf, and below with a piece of white silk.
After having pressed down on the gold leaf the parts of the paper
which are above and below the portrait, the whole is placed in a

FIG. 391. —Experiment of perforating glass.

press (Fig. 393), the screws tightened to render the contact perfect?
and the press is itself placed on the stand of the universal discharger.
When the balls of the discharger are in contact with the tin bands
which extend laterally beyond the press, the discharge is passed
through it, and the volatilized gold leaf produces a blackish impres-
sion on the silk, which reproduces all the cuttings, and the drawing
is thus, so to speak, printed by electricity.

582

PHYSICAL PHENOMENA.

[BOOK

The fusion of metallic wires is a certain proof of the rise of
temperature which accompanies electrical discharges, when they take
place through a conductor. Disruptive discharges, that is to say,
those made through an insulator like air, with the production of a

Fio. 392.— Franklin's portrait experiment.

spark, also give rise to calorific effects, although on receiving the
spark with the finger no heat is felt. Combustible materials, such as
gunpowder and ether, are ignited by sending a spark through them.
This experiment was formerly made in the following manner : — A

FIG. 393. — Press used in Franklin's portrait experiment.

person mounted on an insulating stool, with one hand touched
the conductor of an electrical machine, while with the other he pre-
sented the point of a sword at a short distance from a saucer full of
ether held by another person. The liquid ignited immediately on
the passage of the spark. Watson succeeded in setting lire to ether
by means of a spark issuing from a piece of ice.

CITAP. III.]

ELECTRICAL CONDENSERS.

583

The electrical spark also produces chemical effects of great interest.
If it is passed through a mixture of explosive gases, oxygen and
hydrogen, for example, the explosion is instantaneous. On this fact
is based the construction of Volta's pistol. Figs.
394 and 395 represent a section and exterior view
of this little apparatus ; it consists of a metal
sphero-cylindrical vessel, closed with a stopper and
filled with a mixture of hydrogen and oxygen ; a
brass rod terminated by two knobs crosses the
lower part of the cylinder, from which it is insu-
lated by a glass tube. The apparatus being in
communication with the ground, the exterior knob
of the conductor of an electrical machine is brought
near; the combination of the two gases then takes place with
explosion, and the stopper is forcibly ejected to a distance.

FIG. 394.— Volta's pistol.
Interior view.

Fie. 395.— Explosion of Volta's pistol.

The electrical spark produces a number of chemical reactions,
among which we may mention the formation of nitric acid from
oxygen and nitrogen, and the decomposition of water and of
ammonia.

584

PHYSICAL PHENOMENA.

[BOOK vi.

We have already alluded to the effects of the discharge when it
passes through the organs of man and animals. The shocks are
much stronger, and they affect a larger portion of the body, when
they proceed from more powerful charges ; and we have said that
it is dangerous to receive the charge of a battery formed of even a
small number of Leyden jars. By means of the condenser known
as the fulminating pane, an experiment can be made in which the
shock which the discharge produces has a singular and amusing effect.

t'iu. 3tMj. — Fulmiuatii g pane.

The fulminating pane is nothing more than a rectangular plate of
glass, each side of which is covered with tinfoil : one of the coatings
is insulated, and the other communicates by a small plate with a
wooden frame, thence, by a metallic chain, with the ground. The
other leaf communicates with a source of electricity, and the con-
denser is thus charged ; if, now, a person wishes to pick up a piece of
money placed on the upper leaf, he receives a shock which contracts
his fingers, and prevents him from taking hold of it.

CHAP, iv.] THE PILE OR BATTERY. 585

CHAPTEE IV.

THE PILE OR BATTERY. — ELECTRICITY DEVELOPED BY CHEMICAL

ACTION.

Experiments of Galvani and discoveries of Yolta ; condensing Electrometer —
Description of tlie upright pile — Electricity developed by chemical actions —
Theory of the Pile ; electro-motive force ; voltaic current — Electricities of high
and low tension — Couronne de tasses ; Wollaston's pile ; helical pile — Constant-
current piles ; Daniell, Bunsen, and Grove elements— Physical, chemical, and
physiological effects of the pile — Experiments with dead and living animals.

IN" the experiments hitherto described, the electricity has been
developed on the surface of the bodies by mechanical means ;
such as friction, pressure, and cleavage. These were indeed the only
methods of generating electricity that were known at the end of the
last century, when a fortunate occurrence suddenly revealed to phy-
sicists a new method of producing the mysterious agent, and brought
to light a series of discoveries of the greatest interest, not so much
perhaps in reference to pure science as to practical applications. Two
great names are connected with the origin of the discovery which
added so much to the science of electricity — Galvani and Volta.

Galvani, a learned doctor and Professor of Anatomy in the Uni-
versity of Bologna, was one evening, in the year 1780, very busy in
his laboratory with some friends, making experiments relative to the
nervous fluid of animals. At a short distance from an electrical
machine used in the experiments there were, by accident, some
freshly skinned frogs destined for broth, and one of Galvani's
assistants "inadvertently brought the point of a scalpel near the
internal crural nerves of one of these animals ; immediately all the
muscles of the limbs appeared to be agitated with strong convulsions.
Galvani's wife was present : she was struck with the novelty of the

586

PHYSICAL PHENOMENA.

[BOOK vi.

phenomenon, and she thought that it concurred with the passing of a
spark." l She at once told her husband, who hastened to prove this
curious fact, and discovered that the muscular contractions of the frog
did indeed take place whenever a spark was made to pass, whilst they
ceased if the machine was not in action.

To the Bolognese doctor this observation was the starting-point of
numerous experiments, by which he sought to prove the identity of
the nervous fluid of animals with electricity. In 1786 he was still
continuing this research ; and wishing one day to see if the influence
of atmospheric electricity on the muscles of frogs would be the same
as that of the electricity produced by machines, he hung a certain
number of skinned frogs to the balcony of a terrace of his house. The

lower limbs of these animals
were hooked on the iron of
the balcony by means of a
copper wire, which passed
under the lumbar nerves.
Galvani noticed with surprise
that whenever the feet touched
the balcony the limbs of the
frogs were contracted by sharp
convulsions, although at that
time there was no trace of
a thunder-storm, and conse-
quently no electrical influence
in the atmosphere. These
facts suggested to Galvani
the idea that there existed
a kind of electricity peculiar
to animals, inherent in their organization : and that " the principal
reservoirs of this animal electricity are the muscles, each fibre of
which must be considered as having two surfaces, and as possessing
by this means the two electricities, positive and negative." Hence,
he associated the muscular contractions observed in frogs and other
animals with the shocks given by the discharge of the Leyden jar.

Alexander Volta, then Professor at Pavia, repeated Galvani's
experiments, but without adopting his explanations. According to
1 P. Sue, " Histoire du Galvanisme."

FIG. 397. — Contraction of the muscles of a frog.
Repetition of Galvani's experiment.

CHAP, iv.] THE PILE OR BATTERY. 587

him, the electricity developed is of the same nature as that produced
by ordinary electrical apparatus : it is the contact of heterogeneous
metals which gives rise to the production of electricity, one metal
being charged with positive electricity and the other with negative
electricity, which combine in passing through the conducting medium
of the muscles and nerves.

A discussion was carried on between these two celebrated phy-
sicists, a controversy honourable to both and particularly profitable to
science, which by this means was enriched by a number of new facts.
The invention of the wonderful apparatus which received the name of
the Voltaic pile, at last secured the adoption of the theory of the
Pavian professor ; although Galvani's hypothesis on the existence of
animal electricity has since been partly established, and Volta's ideas
have been greatly modified. This is not the place to give the
history of the controversy, or of the various researches which
accompanied and followed it: we must rather confine ourselves to
the description of the principal phenomena which relate to this branch
of electricity, and to an account of the explanations of them which
are now accepted.

We • have seen that Volta thought that the putting in contact of
two different metals was sufficient to produce electricity ; and for the
purpose of studying the circumstances of this production he invented
an electroscope more sensitive than the gold-leaf electroscope, which
consists of the ordinary gold-leaf electroscope with the conducting rod
surmounted by a condensing plate (Fig. 398). Taking a plate formed
of two pieces of copper and zinc soldered together, he placed the
copper in contact with one of the condensing plates, whilst, with the
finger, the other plate was put in communication with the ground ; as
soon as the communications were broken, the gold leaves diverged,
and he found the lower plate to be charged with negative electricity.
Volta concluded from this experiment that the simple contact of the
two metals was sufficient to develop negative electricity on the
copper, the presence of which was shown by the electrometer ; and
positive electricity on the zinc, which escaped into the ground through
the body of the observer. He was confirmed in this idea by the fact,
that after many attempts, at first unsuccessful, he proved the presence
of positive electricity in the zinc on touching the plate of the
apparatus with that metal. Indeed, he deceived himself; for to

588

PHYSICAL PHENOMENA.

[BOOK vi.

obtain this result, he was obliged to interpose between the zinc
and the copper plate a piece of cloth soaked in acidulated water.
In these various observations Volta did not take into account the
contact of the fingers, always more or less damp, with the zinc, a
very oxidizable metal; nor in the second experiment, the influence
of the acidulated water on the same rnetal. However this may be,
he admitted that the contact of two dissimilar metals, and of any
two heterogeneous bodies in general, gives rise to the development of
a force which he called electro-motive force, because it is opposed to
the combination of the opposite electricities produced on each of these
bodies by the contact of their surfaces Although these theoretical
views are now known to be inexact, the fact which they were adduced
to explain was real ; and this suggested to the illustrious physicist the

construction of an apparatus which
has been justly considered as the
chief discovery of physical science
in modern times — we allude to the
pile which bears his name, the
Voltaic pile or battery, invented
in 1800.

The construction of this appara-
tus is as simple as it is wonderful. •
Two superposed discs, one of
copper and the other of zinc, form
what Volta called an electro-motive
couple; a certain number of these
couples are placed one on the other,
in such a manner that the two

metals are always placed in the same order, the copper at the bottom
and the zinc at the top ;• moreover, each pair of couples is separated by
a disc of cloth soaked in acidulated water. The entire number of these
couples, forming a cylindrical column or pile, is supported between
three glass columns, and rests on an insulating glass disc fixed to a
wooden stand. Such is the pile as constructed by Volta and as it is
constructed at the present day, with the exception of a modification
which will be spoken of presently. The following are some of its
properties : — From end to end of the cylindrical column, each couple
is charged with electricity — positive electricity on the zinc, and nega-

FIG. 398. — Volta' s condenser.

CHAP. IV.]

THE PILE OR BATTERY.

589

tive on the copper — of which we may assure ourselves by the aid
of a condensing electrometer. But the electrical tension varies
according to the distance of each couple from the extremities of
the pile : at the centre this tension is nil ; thence the negative
tension increases to the lower couple, and the positive tension
increases equally to the top couple. The greater the number of
elements or couples, the greater the tension of the electricity at the
extremities of the pile.

In the pile constructed by Volta, and arranged as we have de-
scribed, a copper disc forms the lower extremity, whilst the upper is
terminated by a zinc disc. These two discs are omitted in the pile-

FIG. 399.— Voltaic or column pile.

columns as constructed in the present day, for the following reason : —
Volta believed that the real electro-motive couple was the assemblage
of the two metals, zinc and copper, in contact, and that the disc of
damp cloth served simply as a conductor. It has since been proved
that the electro-motive force is produced at the contact surface of the
damp cloth and the zinc, under the influence of the chemical combi-
nation of the metal and the acid ; the true couple is therefore formed

590 PHYSICAL PHENOMENA. [BOOK vi.

of the zinc arid copper, separated by the liquid with which the cloth
is soaked. Therefore the copper disc of the lower extremity, and
the zinc of the upper extremity, are useless, and are accordingly
omitted. After the omission, the electrical tensions remain distri-
buted as before, — that is to say, the tension is negative on the lower
zinc and positive on the upper copper ; whence the names negative
pole and positive pole which have been given to the two extremities
of the pile.

If the two poles of the pile, thus constructed and charged, are put
into communication by means of a conducting body, the two contrary
electricities combine, and at the moment of contact a discharge takes
place. For instance, on touching the positive pole with one hand
and the negative pole with the other, a shock is felt similar to that
given by the Ley den jar ; then if contact is continued, a peculiar
sensation of heat and trembling is felt. If the two poles are united
by two metallic wires, soldered one to the copper end, and the other
to the zinc end, a spark is produced at the moment when the wires
touch each other ; but after this partial discharge, the pile immediately
re-charges itself, and the same phenomena can be reproduced for a
length of time. It is this property of furnishing electricity in a
continuous manner which characterizes this valuable instrument, and
gives rise to the various effects which we shall presently describe.

Since the time of Volta the pile has been modified, and it is now
constructed under various forms, the most important of which we
shall explain ; but as all these instruments are founded on the same
principle, viz. that of the production of electricity by chemical action,
it is necessary to show by experiment the truth of this principle, as
we now proceed to do.

If we plunge a copper plate into a glass vessel containing nitric
acid diluted with water (Fig. 400), and place the plate in communica-
tion with the lower plate of the condensing electrometer, whilst the
liquid, as well as the upper plate, communicate with the ground, we
observe, as soon as the two plates are separated, that the gold leaves
diverge, and the apparatus is charged with negative electricity. If
the order of the communications is changed, and we connect the acid
by means of a metallic wire with the lower plate of the condenser,
while the other plate and the sheet of copper communicate with the
ground, the apparatus will be charged with positive electricity. If, in

CHAP. IV.]

THE PILE OR BATTERY.

591

place of the copper, a metal is substituted which nitric acid does not
attack, platinum for instance, no electricity will be disengaged.

Similar results are obtained, that is to say, a more or less energetic
disengagement of electricity results, if we excite chemical action
between two bodies. Two solutions, one alkaline and the other acid ;
or, again, two salts, one acid and the other neutral or alkaline,
brought into contact, produce electricity, which is positive on the
body playing the part of acid, and negative on that which plays
the part of base.

Such is the principle of the theory actually adopted to explain the
effects of the voltaic pile : and this accounts for the results obtained
by the illustrious physicist, and for the experiments by which he tried
to demonstrate that a single contact of two heterogeneous bodies suffices
to generate the electro motive force. When the copper and zinc plates
were caused to touch one of the plates of the condensing electrometer,
he did not observe that the cause of the disengagement of elec-
tricity was the chemical action which exerted itself between the
oxidizable zinc and the moist hand.
The electrical development, which
the divergence of the gold leaves
afterwards proves, must be attri-
buted to the oxidation of the metal,
not to its contact with the copper
which plays the part of a simple
conductor. Therefore the real vol-
taic couple is not, as we have
already said, the association of the
two zinc and copper discs, but
rather the zinc, an attackable metal,
and the layer of acid with which the
cloth disc is soaked. The copper is

simply a conductor, on which the developed positive electricit}' in
the acid accumulates, whilst the zinc collects the negative electricity.
Volta perfectly proved, and this fact is independent of his hypothesis,
that the tension of each kind of electricity in the pile-column in-
creases as the two poles are approached. When these poles are put
in communication by two metallic wires, that is to say, conductors,
the phenomena of tension disappear, and the pile is discharged ; but

FIG. 400.— Electricity developed by chemical
action.

592 PHYSICAL PHENOMENA. [BOOK vi.

in proportion as the recombination of the two electricities takes place,
the productive cause, which is the chemical action of the sulphuric
acid on the zinc, continues to act, and the pile thus becomes a
constant source of electricity, so that it is possible to assimilate this
action to an incessant flowing of the two kinds of electricity, negative
electricity towards the positive pole, and positive electricity towards
the negative pole, through the interpolar wire. These two currents
evidently pass in contrary directions through the couples themselves.

It is usual to give a direction to this double current, considering
only the movement of the positive electricity. This is called the
current of the pile, the direction being, as we have just seen — and it is
important to remember this- — from the negative to the positive pole
in the interior of the pile, and from the positive to the negative pole
in the portion of the circuit formed by the connecting wires, which
are sometimes called rheophorcs, or carriers of the current.

We will now speak of the difference in the phenomena of electri-
city, as we have studied them in the electrical machine and Leyden
jar, and those shown by the voltaic pile. In the first apparatus, the
electricity developed remains at rest on the surface of the conduc-
tors, which has given it the name of static electricity. On the other
hand, the electricity which is constantly produced in a pile and passes
through the conductors, is electricity in motion, whence the name
dynamic electricity. Nevertheless, if we analyse more closely these
two classes of phenomena, we should see that it would be better to
characterize them in a different manner. When by the help of a
conductor we unite the contrary electricities which have accumulated
on the two coatings, interior and exterior, of a Leyden jar, there
is also, as in the pile, an electric current; but this current lasts
but a moment, because the cause which developed the electricity
no longer exists. In the pile, the renewing of the electricity takes
place in proportion to the recomposition, and the current is con-
tinuous. Moreover, the phenomena produced under these two
conditions have a very great analogy, and the differences which they
present result mainly because, in the first case, the electricities which
combine with each other are at very high tension, while, in the
second case, they gain in continuousness what they lose in intensity.
It is now considered preferable to substitute for the names which
we have just mentioned, those of electricity of high tension, which is

CHAP. IV. 1

THE PILE OR BATTERY.

593

that of the ordinary electrical machine, and electricity of low tension
which is the electricity of the pile.

Volta's pile has received various forms, devised with a view of
rendering it more convenient, and more especially to increase its
energy. In the original column pile, the energy is diminished by
the escape of the liquid which the weight of the superposed elements
causes to ooze to the outside ; this produces secondary outer currents
at the expense of the principal current. In the various forms of
battery we are about to describe, the principle is precisely the same
as that of the voltaic pile.

The trough pile invented by Cruikshank is formed of plates of
zinc and copper soldered together, and arranged parallel to each other
in a wooden box or trough. The elements, insulated by mastic or
resin, are separated into compartments, which are filled with acidu-
lated water when the pile is about to be used. By this arrangement
secondary currents are no longer produced.

FIG. 401. — Crown or cup pile.

Imagine a series of cups or glasses filled with acidulated water,
and arched plates formed, in one case of copper, and in the other of
zinc, the extremities of which are inserted in the liquid of two con-
secutive glasses, so that, in each of these, there are two plates, one of
copper, and the other of zinc. On uniting by two metallic wires or
rheophores the copper and zinc plates of the extreme vessels, we have
the cvp pile invented by Volta, which is also called the crown pile,

z z

594

PHYSICAL PHENOMENA.

[BOOK vi.

because the elements are generally arranged in a circle, as shown
in Fig. 401. Wollaston devised the following arrangement : — A rect-
angular sheet of copper is curved in such a manner as to envelope
within it a zinc plate, from which it is separated above and below
by pieces of wood. A band of copper is soldered to the upper part of
the zinc, and bent on both sides at right angles, so as to connect the
copper plate of the next element ; lastly, all these bands are fixed
to a cross-piece of wood, which can be raised or lowered at will,
together with all the elements. Vessels filled with acidulated water
are placed under each element ; by lowering the cross-piece the pile
can be worked (Fig. 402). The advantage of Wollaston's pile, besides
the facility for working it, is the great extent of zinc surface in
contact with the acid.

FIG. 402. — Wollaston's pile.

We may mention also the piles of Muncke, and of Oersted, and
the spiral pile which was invented by Hare ; the latter has great
surface with small bulk. It is formed of two long wide bands of
copper and zinc, which are both wound round a wooden cylinder ; but
the two consecutive spirals of the two metals are insulated by rods of
wood or pieces of cloth. When the pile is about to be used, the whole
is immersed in a pail full of acidulated water.

In the piles just described the electrical current is variable ; at the
commencement of the action its intensity is as great as possible ; but
different causes tend to progressively diminish the energy. Under
the influence of the current, water partially decomposes ; the hydrogen,

CHAP, iv.] THE PILE OR BATTERY. 695

one of its component gases, is disengaged on the zinc as well as on
the copper, and forms on the surface of the metal a gaseous stratum,
which diminishes the chemical action. Partial currents are also
formed which interfere more or less with the electricity disengaged,
and thus weaken the interpolar current. Lastly, as by the very fact
of the chemical reactions there is combination of oxide of zinc with
sulphuric acid, producing a salt, sulphate of zinc, it is evident that the
liquid is more and more impoverished as regards acid. Endeavours
have been made to render the currents of the piles constant, by
modifying the construction of the electro-motive couples. Hence the
constant current piles, which are distinguished from variable current
piles principally by the placing of each element of the couple in
contact with a particular liquid, to prevent the formation of hetero-
geneous deposits on each of them.

FIG. 403. -Spiral pile.

The batteries most employed are those of Danieil, Bunsen, and
Grove. The electro-motive couple of Daniell's pile is represented
in Fig. 404. It consists of two vessels, the outer one of glass or
earthenware, and the other, placed within the first, of porous earth.
Between the two vessels, water acidulated with sulphuric acid is
poured, and in the porous vessel a solution of sulphate of copper.

In the first liquid a wide plate of amalgamated zinc, of cylin-
drical form, is immersed, and in the other a copper cylinder. The

z z 2

596

PHYSICAL PHENOMENA.

[BOOK vi.

following is the manner in which the disengagement of the two
electricities takes place on the copper and zinc.

Water is decomposed ; its oxygen attacks the zinc and forms oxide
of zinc, which combines with the sulphuric acid of the liquid of the
outer vessel ; the zinc acquires a negative electric tension. The
hydrogen of the water, passing through the porous vessel, attacks the
sulphate of copper, the oxide of which is decomposed ; and the copper
is precipitated in the metallic state on the copper cylinder, which
acquires a positive electric tension. Each reaction engenders a current,
the first from the zinc to the acid, the second from the copper to the
solution which surrounds it. The electro-motive force of Daniell's
couple is the resultant of these two contrary forces. The final current
is not of great strength, but it remains sensibly constant if the pre-
caution has been taken to place crystals of sulphate of copper in the

FIG. 404.— Couple of Daniell's battery.

porous vessel. The zinc and copper keep their surfaces fresh without
any deposit of foreign matters.

Bunsen's couple is arranged like Daniell's, but the copper cylinder
is replaced by one of gas retort carbon, and the solution of sulphate
of copper by nitric acid. Bunsen's couple is preferable to Daniell's on
account of the strength of the current, but it is inferior in being less
constant.

CHAP. IV.]

THE PILE OR BATTERY.

597

Grove's battery is constructed as follows : — A vessel composed of
any material not attacked by sulphuric acid is partially filled with
that acid diluted in the proportion of one acid to eight water. In
this vessel is inserted a zinc plate which is curved in the form of
an U. Into this U is inserted a porous vessel containing nitric
acid and a plate of platinum. The platinum of one cell is connected
with the zinc of another, and so on. This battery is one of very
great power.

By uniting several similar couples by their contrary poles,
Darnell's, Bunsen's, and Grove's batteries are formed, the strength
being proportional to the number of elements thus united. The
negative pole in both piles is the zinc of the last element ; and the
positive pole the last copper in Daniell's pole, or the last platinum

FIG. 405.— Couple of Bunsen's battery.

plate in Grove's, or the last carbon in Bunsen's pile, as shown in

Fig. 406.

We may now describe some of the more remarkable phenomena
which give rise to the production of electricity of low tension ; that is
to say, of electricity produced by voltaic piles under the influence of
chemical action. Heat, light, chemical combinations and decomposi-

508

PHYSICAL PHENOMENA.

[BOOK vi.

tions, nervous shocks and various physiological effects, are among the
various phenomena which are manifested by the wonderful apparatus
with which Volta, sixty-eight years ago, enriched science.

The calorific effects of piles are much more intense than those
obtained by the discharge of electrical apparatus at high tension, as
the following experiments will show : if the circuit of a few couples
of Wollaston's battery is closed, by connecting the rheophores with a
metallic wire of small diameter and a few centimetres in length, the
wire becomes heated under the influence of the current which passes
through it, soon it acquires a red heat, then melts, and is volatilized.
With a pile of 21 of Wollaston's elements, platinum wires of 5 milli-
metres in diameter and 7 centimetres in length can be melted. The
constant current poles are more powerful still ; with 50 of Bunsen's
elements iron or steel wires, a wire, a foot in length and of the size
of a knitting needle, fuses and burns, sending out brilliant sparks
in all directions. The size of the elements has more influence on the
intensity of the heat effects than the number of couples used.

FIG. 406.— Pile formed by five Bunsen's elements.

Davy fused various metals, and observed the. curious phenomena
of coloration which proceed from the combination of metals with
oxygen, when we use a battery possessing large surface. Iron
burns with a red light ; zinc gives a flame of a bluish white ; gold,
yellow,; silver, white, with a greenish tint on the edges; copper,
green ; tin, purple ; lead, yellow ; platinum alone melts without being
oxidized, and falls in drops of dazzling brightness.

We have seen that different metals do not conduct electricity
equally well : those which offer the greatest resistance to the current

CHAP, iv.] THE PILE OR BATTERY. 599

become heated to the greatest extent. If we take two wires of equal
diameter, formed of different metals, one of which becomes incandes-
cent, while the other remains dark, the latter is always formed of the
better conducting metal. This fact has been proved by forming a
metallic chain of links which are alternately silver and platinum, and
by attaching the two extremities of the chain to the rheophores of a
pile ; when the current passes, the platinum begins to redden, becomes
incandescent, and even melts, whilst the silver remains unchanged.
The conductibility of the latter metal for electricity is 100, whilst
that of platinum is only 8. It is for this same reason, that is to say, on
account of the different resistance offered to the passage of the same
current, that two wires of the same metal and unequal diameter heat
unequally ; as the larger offers less resistance, it consequently heats
less than the smaller. When a metallic wire, raised to a red-heat by
the voltaic current, is plunged into water, the incandescence ceases,
which is but natural, since it transfers part of its heat to the liquid,
but a curious experiment by Davy proves that this phenomena has
also another cause, having made a metallic wire red-hot by means
of the voltaic pile, he cooled a portion of it by touching it with a
piece of ice ; immediately the part not touched was raised to a white
heat and melted. The reason seems to be that the cooling diminishes
the resistance of the wire, and thus increases the intensity of the
current, which then becomes strong enough to melt the portion of the
wire which the first intensity had only raised to redness. In the case
of the wire immersed entirely in water, the incandescence of which
ceases, the phenomenon is complete ; there is cooling by contact
with the water, diminution of the resistance of the wire and increase
of the intensity of the current; and the two latter causes produce
contrary effects.

Voltaic batteries produce electricity at low tension ; it is therefore
not astonishing that the reunion of the rheophores of a charged pile
should not produce a spark, or, at least, only a small one. But if a
very powerful pile is used, composed of a great number of elements,
and if instead of closing the circuit by placing the wires in contact a
small space is left between their extremities, sparks will appear close
upon each other, which form a continuous light if the two wires are
terminated by charcoal points. This continuous light is known as the
voltaic arc. Davy, with a pile of 2,000 couples, each having about

PHYSICAL PHENOMENA. [BOOK vi.

sixty square inches of surface, obtained a dazzling light, which appeared
in a continuous manner in the space between two charcoal points. The
space was at first only half a millimetre ; but the light once produced
he could separate the coal points to a distance of 11 millimetres. He
then saw a phenomenon of great beauty. The electric light spread
itself between the two electrodes in the form of an arch, the convexity
being above, and of such intense brightness that the eye could scarcely
endure it. In vacua the length of the arc is greater than in air.
Since the time of Davy, the production of the voltaic arc lias been
rendered more easy, and, thanks to the induction apparatus which we
shall describe in a succeeding chapter, it has also been employed
for lighthouses. The arc develops a heat of extreme intensity ;
metals melt in it like wax in the name of a lamp.

The most refractory bodies have been melted and volatilized by
M. Despretz, at first with a pile of 600 couples, then by using an
induction apparatus. Oxides of zinc and iron, lime, magnesium and
. aluminium were reduced to globules ; graphite, volatilized, deposited
a dust on the electrodes which, when examined with the microscope
appeared as very small octahedral crystals ; with this powder, rubies
have been polished ; it has therefore been concluded that the graphite
— which, like the diamond, is of pure carbon — had been crystallized
under the influence of the intense heat of the arc, and changed into
very small diamonds.

The chemical effects of the pile present the greatest interest.
Decomposition of water is one of the most important. To effect
this the apparatus represented in Fig. 407, called a Voltameter,
because the quantities of water decomposed in a given time by the
voltaic current serve to measure the intensities of these currents, is
employed. It consists of a glass vessel, the bottom of which is
covered with mastic and pierced by two platinum wires which unite
at the extremities of the rheophores of the pile ; the vessel is filled
with water, with the addition of a few drops of sulphuric acid, which
renders the liquid a better conductor. Two graduated glass tubes
cover the platinum plates. When the current passes, bubbles of gas
are seen to be disengaged round the plates and to rise to the top of
each tube. One of these gases is hydrogen, the other oxygen, and
the volume of the first is always double that of the second. More-
over the disengagement of the oxygen always takes place from the

CHAP. IV.]

THE PILE OR BATTERY.

601

plate which is attached to the rheophore of the positive pole, whilst
the hydrogen is disengaged at the negative pole.

By the aid of the pile, Davy succeeded in decomposing the oxides
of the alkaline metals, potash for example, from which resulted a new
metal, potassium. A great many other chemical compounds, acids
and bases, have been resolved into their elements by the influence of
the voltaic current, and chemistry possesses in it a new and powerful
means of analysis. We may mention as another example of de-
composition, that of a metallic salt : we shall see presently the
importance of the applications which the arts have made of this
mode of electrical motion.

The salt known in chemistry as sulphate of copper, is a compound
of two binary combinations : on the one hand, sulphuric acid, and on

FJO, 407.— Decomposition of water by the voltaic pile.

the other, protoxide of copper. Sulphur and oxygen form sulphuric
acid ; copper combined with the same gas, oxygen, forms the metallic
oxide. Let us examine how the separation of these elements can
be made under the influence of electricity disengaged from the
rheophores of a pile.

In a vessel which holds a solution of sulphate of copper, two
platinum plates attached to the rheophores of the pile are immersed.
Under the influence of the electric current, bubbles of oxygen are
seen to be disengaged around the plate which corresponds to the
positive pole — this is called the positive electrode — and the copper is
deposited in a metallic state on the surface of the plate which forms

3 A

602 PHYSICAL PHENOMENA. [BOOK vi.

the negative electrode. Thus the salt has been decomposed ; its
base, separated from the acid, is itself decomposed into oxygen and
copper : as the sulphuric acid became free, it was carried towards the
positive electrode. We may satisfy ourselves of this by testing with
litmus paper different parts of the solution, and we shall see that the
red tint of the test paper is strongest in the vicinity of the positive
electrode. The phenomena of chemical decomposition by voltaic
electricity are extremely numerous and complex ; in fact, they would
require a volume to describe them. We will confine ourselves to the
indication of a singular fact which always accompanies electrolytic
action (this is an expression deduced from the word Electrolysis, by
which Faraday distinguished decomposition by the pile). When the
electrodes have been in use some time, if they are taken out of the
saline solution, plunged into pure water, and put in communication
with the wires of a galvanometer, it will be remarked with this
instrument, which will be described shortly, that a current passes
in a contrary direction to the original current ; that is to say, from
the negative to the positive electrode. It is then said that the
electrodes are polarized. The secondary current of which we speak
is only temporary, and is due to the accumulation on the electrodes
of the deposit produced by electrolysis ; it ceases as soon as these
deposits are destroyed by the effect of the fresh chemical actions
engendered under its influence.

Commotions or nervous shocks, caused by the passage of a current
from a pile through the organs of men or animals, are greater as the
pile is formed of a larger number of couples. The effect produced
depends only on the tension of the pile, a tension which increases
with the number of the elements, the surface being unable to effect
a like result. It is dangerous to be exposed to the shock of a powerful
pile. Gay-Lussac felt for more than a day the violent shock he
received by touching the two rheophores of a trough pile of 600
couples. The sensation is perceived with the greatest strength at the
moment when the circuit is closed. Then the arms and chest are
shaken, but afterwards only a sort of trembling is felt in the muscles
of the arms and hands ; when the communication is at last broken, a
fresh shock is felt, more feeble than the first. Moreover it is neces-
sary to distinguish two sorts of physiological effects of the pile ; the
simple muscular contraction, without pain, and a sharp and painful

CHAP. iv.J THE PILE OR BATTERY. 603

sensation, without contraction. It is now known that the nerves are
divided into sensitive nerves and motor nerves : the first have the
function of transmitting the sensations to the nervous centres, the
brain and the spinal cord ; while the motor nerves execute, so to
speak, the orders which come from the brain itself, and give motion
to the muscles. These two kinds of nerves, the one motor and the
other sensory, are inserted by two kinds of root, and are united for a
certain space ; they are then separated and divided into two branches,
one carrying sensibility to the organs, the other giving them move-
ment. Now, if the circuit is closed after having placed one of the
rheophores on the common fibres of the two orders of nerves, there is
both contraction and painful sensation in the animal subjected to
the experiment. But there is only contraction if the ramifications
of the motor nerves are touched, and only pain if the ramifications
of the sensory nerves are first touched by the wire.

The physiological effects of the pile have been the object of
numerous and very interesting experiments, both on living and dead
animals. Galvani and his kinsman, Aldini, professor at Bologna, had
the honour of commencing this fruitful study of the influence of
electricity on animals. They showed that the passage of the current
produces in the muscles of dead animals contractions frightfully like
the movements which they have during life. Aldini's experiments
on the bodies of two criminals beheaded at Bologna, in 1802, are
particularly celebrated ; those also of Dr. Andrew Ure on the body
of a criminal an hour after he was taken from the gibbet. One of
the nerves of the eyebrow was put into connection with one of the
wires of the pile ; the heel with another pole : when the face of the
criminal contracted in such a hideous manner that one of the assistants
fainted. No expression can describe the horror of the observers in
the terrible scene which followed this experiment.

The action of the pile on living beings is not less curious ; and
its effects interest us more, since we have discovered its good
influence in the curing of certain illnesses, principally nervous
affections. The action of the voltaic current on the organs of
the senses produces precisely the sensations belonging to each of
them. By exciting the optic nerves, the sensation of light is pro-
duced, and that of sound if the nerves of the ear are touched.

3 A 2

C04 PHYSICAL PHENOMENA. [BOOK vi.

CHAPTER -V.

ELECTRO-MAGNETISM.

Action of a current on the magnetic needle ; Oersted and Ampere — Schweigger's
multiplier ; construction and use of the galvanometer — Action of magnets on
currents — Action of currents on currents — Influence of the terrestrial magnetic
force — Ampere's discoveries ; solenoids ; the electrical helix ; theory of mag-
nets— Magnetism of soft iron or steel discovered by Arago ; magnetization by
means of helices — The electro-magnet ; its magnetic power ; its effects.

rnWENTY years after the discovery of the voltaic pile a new fact
JL of great importance was brought to light by Oersted, a Swedish
physicist, professor in the University of Copenhagen : he discovered
that the electric current acts on the magnetic needle. For some time
the existence of a relation between magnetic and electrical phenomena
had been suspected : the perturbations undergone by the compass on
board vessels struck by lightning had been noticed ; as also on those
whose masts had presented the electrical phenomenon known as the
fire of Saint Elmo ; it was known that the discharges of electric
batteries agitated a magnetic needle placed in their vicinity. But
these facts afforded but vague ideas as to the actual correlation.
In 1820, the year in which Oersted made his discovery, Ampere
studied and propounded the laws of this action, and showed, moreover,
that the currents themselves act on other currents.

Lastly, Arago discovered the magnetism of soft iron and that of
steel under the influence of the current of the voltaic pile. These
experiments were the starting-points of a multitude of new ones,
which in a short time changed the aspect of this branch of science,
by demonstrating that magnetism and electricity are varied manifesta-
tions of the same cause. We shall see hereafter, that the discoveries
which revealed the real nature of magnetism, and gave so much

CHAP. V.]

ELECTRO-MAGNETISM.

605

advance to theory, have not been less fruitful in ingenious and useful
applications.

Let us now return to Oersted's experiment. Imagine a magnetic
needle suspended on a pivot, and moveable in a horizontal plane ;
we know that it will then place itself in the magnetic meridian,
making a constant angle with the north and south geographical
meridian line. If we then place parallel to the needle, and at a
short distance above, a metallic wire whose extremities are joined to
the rheophores of the pile, we notice that so soon as the current passes,
the needle is deviated from its position ; it leaves the magnetic
meridian and sets itself across the current. If, instead of placing
the wire above the magnetic needle, it is placed at the same
distance below it, the needle is again deviated and sets itself

FIG. 408. — Action of an electrical current on the magnetic needle.

across the current. In repeating the same two experiments and
changing the direction of the voltaic current, — that is, if it first passes
from south to north, it is now caused to pass from north to south, —
we observe that the needle is again deviated and sets itself at right
angles to the current, but in precisely opposite directions to those
which it assumed under the influence of the direct current.

Again, if, instead of placing the wire parallel to the needle, it
is placed perpendicularly to the horizontal plane opposite one or
the other pole, the needle will be seen to undergo again the same
deviations, corresponding to the four fresh dispositions which can
be given to the voltaic current, — from top to bottom, bottom to top,
and opposite either to the southern or northern pole of the needle.

Such are Oersted's experiments, and Ampere succeeded in
formulating, in a single statement, the law which governs them.

606 PHYSICAL PHENOMENA. [BOOK vi.

He conceived the ingenious idea of personifying the current, by
figuring it as a person laid along the current, whose face, in all
possible positions, is always turned towards the centre of the
needle. The current, which passes from the positive pole of the
pile to the negative pole through the wire, is supposed to enter
by the feet of the person and to come out at his head ; then the
current is found to have a right and a left, which are those of the
person himself: therefore, the following is the simple statement
by which Ampere has connected the various conditions which
furnish Oersted's experiment : —

When an electric current acts on a magnetic needle, the southern
pole of the needle — which is always that which is directed towards
the north — is deviated towards the left of the current.

Thus, if the current passes parallel to the needle, and from

FIG. 409.— Deviation of the southern pole FIG. 410.— Deviation to the left of the current,

towards the left, under the influence Lower curreut.

of the upper current.

south to north, the case is met by that of the two figures, 409
and 410. In the case of the upper current, the south pole A is
deviated to A! to the left of the current, — that is, towards the west ;
if the current passes below the needle it is always to A' — to the
left of the current that the south pole A is deviated, but now
this pole moves towards the east. If the direction of the current
is changed, still remaining parallel to the needle, — that is to say, if
it passes from north to south, — the southern pole will be deviated
towards the east, in the case of the upper current, and to the
west, in the case of the current placed below the needle. Lastly,
when the current is vertical, it can be either ascending or descend-
ing, and placed either opposite the northern or southern pole of
the magnet. In the case represented in Fig. 411 the southern
pole is seen to deviate to the east; that is, to the left of the

CHAP, v.]

ELECTRO-MAGNETISM.

607

„->/

411. — Deviation to the left of tho

current, vertical current.

current. We will leave the reader to find the direction of the
needle in the other cases ; a task which has been rendered easy by
Ampere's law.

The laws which regulate these observations were studied by
Biot and Savart and by Laplace. Bearing in mind the fact that
the influence of the current depends on its intensity and, conse-
quently, on the surface of the couples of
the pile employed, it diminishes in pro-
portion as the distance from the needle
increases. It must not be forgotten that
in the presence of a voltaic current, the
needle is subjected to two influences at
the same time, viz. that of the current
itself, and that of the earth, which acts
on the needle like a magnet ; the devi-
ations observed are, therefore, an effect
resulting from these two simultaneous

actions. If, by any means, we can render the direction of a magnetic
needle independent of the action of the earth — it is then called an
astatic needle — the current deviates the needle to a right angle, what-
ever may be its intensity. The deviation then indicates only the
presence of the current, without proving its energy.

Let us now see how we can utilize the action of electrical currents
on the magnetic needle, in the construction of apparatus which serve
both to prove the presence of small currents, and to measure their

intensity. We will first describe the
apparatus called Scliweigger 's multiplier,
from its inventor:^—

It consists of a wooden frame (Fig. 412)
round which a copper wire is wound a
great number of times ; this metallic wire
'\ is entirely covered with an insulating
\- substance, gutta-percha, silk, cotton, &c.,
so that an electric current entering by
one of the extremities of the wire, and
issuing from the other, cannot pass from one spiral to another without
having traversed the whole length : in a word, it is obliged to pass

FIG. 412. — Schweigger'8 multiplier.

through all the successive windings. If the frame is placed verti-

COS PHYSICAL PHENOMENA. [BOOK vt

cally on one of its sides, in the plane of the magnetic meridian, and
if a magnetic needle is placed in the inside, suspended freely on a
vertical pivot, a good instrument will be obtained for showing, by
the deviation of the needle, the existence of an electrical current,
however slight it may be. To effect this, it is sufficient to attach
the extremities of the wire of the multiplier to the two rheophores of
the pile or of any voltaic circuit; so soon as the circuit is closed,
the presence of the current will manifest itself by a greater or less
deviation of the needle.

We will now analyse this effect, and examine how the action of
the current is multiplied by the arrangement we have just described,
and, for this purpose, we may first consider one of the circuits of
the wire wound round the frame ; the current passes from M to N,
then to Q and P, and at n leaves the needle. Now, if we compare

it with Ampere's statement, we shall
^^.^^ see that each of the four portions of the

current tends to deviate the southern

pole from a to a, consequently towards

the east, or, in other words, to the front

of the figure; each of them acts like

FJO. 413. — Concurrent actions of the dif- , . , -> , vi

ferent portions of the wire in the an insulated current, or better, like an

multiplier.

indefinite portion of the current near

the needle. The total deviation will be then stronger than if the
current only followed one of the sides of the rectangle. ]STow, at
the following winding, the current acts again in the same manner,
and it is the same for all the successive windings, so that its in-
fluence on the magnetic needle is multiplied by the number of the
windings of the wire. Hence the name of multiplier is given
to the instrument.

The magnetic needle is in this experiment, as we have already
stated, submitted to two forces : the directive action of the earth,
in virtue of which it places itself in the magnetic meridian ; and
the action of the current, which tends to cause it to assume a posi-
tion at right angles to the first. The deviation of the needle is
produced by the resultant of these two actions. To increase the
deviation, and to give a greater sensibility to the multiplier, Nobili
conceived the idea of substituting for the magnetic needle a system
of two parallel magnetic needles, fixed on the same axis, with

CHAP. V.]

ELECTRO-MAGNETISM.

GOO

their poles of the same name placed in contrary directions. The
suspension being by a silk thread without torsion, if the needles
have the same magnetic force, their system will be astatic; that
is to say, will remain in equilibrium,
whatever may be its angle with the
meridian. A system exactly astatic would
not fulfil the end which is proposed,
which is to measure the intensity of the
currents by the deviation, as then the
deviation would always attain the maxi-
mum of 90°, whatever the power of the Fla 414-s>nSesf tw° astatic
current. But if one of the needles, the

lower one for example, is a little more magnetized than the
upper one, the system will continue to be influenced by the
earth ; but this action will be very feeble, and therefore the

Fig. 415.— Galvanometer.

action of the currents through the intervention of the multiplier
will be, on the contrary, considerable. The introduction of the
compensated needles in Schweigger's multiplier led Nobili to
the construction of the galvanometer (Fig. 415), the most delicate

610 PHYSICAL PHENOMENA. [BOOK vi.

apparatus for determining the existence, strength, and direction of
weak electrical currents. The following is the manner in which
this instrument is used : —

The ivory frame around which the insulated wire is wound, and
which is below the dial, can be moved in a horizontal plane by an
outside screw ; and it is first brought into a plane of such a nature
that the zero of the graduation of the dial corresponds to one of
the extremities of the needle. It is now certain that the rounds
of copper wire are parallel to the two needles of the system. The
apparatus is furnished with levelling screws, so that it can be placed
horizontally ; a,nd a glass shade protects the suspending thread and
the needles themselves against the agitation of the exterior air.
The frame includes a rectangular ivory plate, which has two brass
buttons, at each of which terminates the extremity of the two wires
of the multiplier. To these buttons, or binding screws, the rheophores
of the current, the direction and intensity of which are to be deter-
mined, are attached : as soon as the circuit is closed, and the current
passes along the rounds of wire, the upper needle is seen to deviate
to the right or left of its position of equilibrium; the direction
of this deviation indicates, according to Ampere's law, the direction
of the current.

The intensity of the current is measured by the arc which
either of the extremities of the needle has traversed, starting from
the zero of the graduation. It has been found that, if the devia-
tion does not exceed 20°, it is sensibly proportional to the intensity
of the current.

We have just seen the action of voltaic currents on the magnetic
needle, and how this influence has been utilized in constructing an
apparatus of extreme delicacy, to show the direction and intensity of a
certain current. We may now state that magnets exercise on currents
an action equal to that to which they themselves are submitted, but
in a contrary direction. Thus, when a strongly magnetized magnetic
bar A B (Fig. 416) is placed in a horizontal position below or ahove
a metallic wire forming a voltaic circuit, and free to turn round the
points of suspension, the wire is seen to set itself across the magnet, in
such a manner that the south pole of the bar is always to the left of
the current which is nearest to it. When the direction of the current

CHAP. V.]

ELECTRO-MAGNETISM.

611

is changed by the reversal of the rheophores which terminate the two
extremities of the wire, the wire immediately makes a rotation
of 180° on itself; the southern pole of the latter is still to the left
of the current, according to Ampere's law.

We have now arrived at Ampere's beautiful discovery, which
immediately followed that of Oersted's, as to the action of voltaic
currents on each other. We will confine ourselves to the statement
of the principal laws which govern the reciprocal influence of
currents, laws the experimental verification of which is easy, in the

Repulsions.

Attractions.

FIG. 416. — Action of a magnet on a current.

FIG. 417. — Law of the attraction and repulsion
of a current by a current.

numerous particular cases which they comprehend. Ampere has
demonstrated that : —

1st. Two parallel currents, which pass in the same direction,
attract each other: while they repel each other if they pass in a
contrary direction.

2nd. Two non-parallel currents attract each other, if at the same
time loth approach or recede from the apex of the angle formed ly
the ends produced ; they repel each other, if one of the currents
approaches the apex of the angle, whilst the other recedes from it.

Fig. 417 represents the three cases of attraction and two cases
of repulsion to which these laws refer. Thus then, on the one hand,
electrical currents act on magnets, and magnets act on currents :
while, on the other hand, currents act on each other. Hence, there is

612 PHYSICAL PHENOMENA. [BOOK vi.

only a step to assimilate magnets with, currents ; Ampere has indi-
cated this, and has brought to the help of theory the control of
experiment. He discovered that the earth itself acts on the currents ;
that if a rectangular instrument similar to that of Fig. 416 is left
to itself, and an electrical current passed through it, the apparatus
turns round on its vertical axis and places itself spontaneously
across the magnetic meridian ; the ascending portion of the current
is carried to the west and the descending portion to the east.
M. Pouillet, by some clever arrangements, has shown that an insu-
lated vertical current, moveable round an axis which is parallel to
it, is transported of itself to the magnetic west or east, according as
it is ascending or descending, whilst the action of the earth on the
horizontal branches of Ampere's apparatus is nil. To determine the
nature of these facts Ampere constructed a static apparatus, — this is
to say, a magnetic system indifferent to the action of the terrestrial
globe ; then causing a fixed current to act on it, placed horizon-
tally in a direction perpendicular to the magnetic meridian, from
east to west, he saw that the action of this current was precisely
the same as the action of the earth. He concluded that the magnetic
action of the earth on the magnetic needle is due to electrical
currents which continually circulate perpendicular to the magnetic
meridian, their direction being from east to west. These various
currents, whatever may be their number, may be considered as com-
posing a single current ; and experiment shows that, in our latitudes,
its position is situated towards the south.

Pursuing these beautiful generalizations, Ampere showed that a
magnet may be assimilated to an assemblage of circular vertical and
parallel currents passing in the same direction. An assemblage of
such currents indeed — experiment will show us — when freely sus-
pended so as to be able to turn in a horizontal plane, places itself, when
submitted to the action of the earth, in the magnetic meridian ; in
fact, it behaves exactly like a magnetic needle. Ampere constructed
a helix or electrical magnet in this way : — He took a metallic wire
and rolled it round a cylinder in equidistant coils, giving it the form
represented in Fig. 418 ; he then brought the two extremities of the
wires longitudinally above the coils, and curved them in such a way
that the whole could freely turn round a vertical axis ; next, he at-
tached the two ends of the wire to the rheophores of a pile. When the

CHAP. V.]

ELECTRO-MAGNETISM.

C13

current passes in the direction marked by the arrows, the solenoid —
the name given to the apparatus by Ampere — places itself in a position
of stable equilibrium ; each coil is in a vertical plane, its direction
being from magnetic east to west ; the axis of the solenoid coincides
then with the magnetic meridian, exactly like a magnetic needle. If
the direction of the current is changed, the solenoid is seen to be dis-
placed ; and after having moved through 180°, it places itself in its
original position, its longitudinal axis being always in the magnetic
meridian, but it is turned about. Lastly, an element of the solenoid,
suspended so that it is able to turn freely -round an axis perpendicular

Wes

North.

— - East.

\8outh.
Fio. 418.— Direction of a solenoid in the meridian, under the action of the earth.

to the magnetic meridian, assumes an inclination which is precisely
equal to that of the magnetic needle.

Thus, ordinary magnets, and solenoids or electrical magnets, con-
duct themselves in the same manner when under the influence of the
magnetic action of the earth. But the analogy has been pushed
further; Ampere has shown that the extremities or poles of two sole-
noids exercise on each other attractions and repulsions of the same
nature as the attractions and repulsions of the poles of magnets:
poles of the same name of solenoids repel each other ; while poles of
contrary names attract each other. Lastly, the same actions manifest
themselves, if the pole of a solenoid is presented to one or other of the

614

PHYSICAL PHENOMENA.

[BOOK vi.

two poles of a magnetic needle. The similarity is complete, and
Ampere was able to form his theory of magnetism in all its exactness,
a theory which assimilates magnetic phenomena with dynamic
electrical phenomena. The following is a brief r6sum6 of this
beautiful theory : —

The terrestrial globe is continually traversed by numerous electrical
currents, induced perhaps by chemical action. These various currents,
with directions and intensities probably different and variable, pro-
duce on magnets the same effect as a single current, resulting from
the composition of the elementary currents, circulating from east to
west, in a direction contrary to the earth's movement of rotation. A
magnetic substance, iron, steel, &c., also becomes the seat of elemen-
tary electrical currents, circulating round certain groups of atoms.
In soft iron, and in magnetic bodies which are not endowed with
polar magnetism, these currents move in all directions, so that the

oooo

FIG. 419. — Particular currents of magnets. FIG. 420. — Resulting currents at the surface

of a magnet.

resulting effect is nil. In magnets, on the contrary, the particular
currents have all the same direction ; for example, they circulate as
the arrows indicate in Tig. 419, in which is shown a transverse section
of a magnetic bar. In the neighbouring or contiguous portions in
&, V, a, a', &c., the currents are of contrary directions, and are de-
stroyed ; so that the total effect is reduced to the exterior effect, which
leads us to consider the contour of each edge as being traversed by a
single current. The same effect will take place in all the sections,
and the magnet will be constituted as indicated in Fig. 420.

We therefore see that, according to Ampere's theory, every magnet
may be considered an equivalent to a solenoid.

In regard to magnetic substances, such as soft iron, the vicinity of
a magnet causes them to momentarily acquire polar magnetism, by the
same action that the currents of solenoids exercise on the currents of
which they themselves are a part. This influence modifies the direc-
tion of these elementary currents, and makes their resultant no longer

CUAP. v.] ELECTKO-MAGNETISM. 615

nil; thus is produced induced magnetism. "We shall find, moreovei,
that permanent magnetism is perfectly explained by Ampere's theory •
but in this case, experiments must instruct us, and they will reveal
to us phenomena of the greatest interest.

In September 1820, Arago, a short time after Oersted's and
Ampere's discoveries, made the following experiments : — He inserted
into a mass of iron filings a copper wire which united the two poles
of a pile ; on drawing out the wire without interrupting the current, he
saw its surface covered with particles of iron filings, arranged trans-
versely ; as soon as the current was interrupted, the particles detached
themselves from the copper and fell. To assure himself that this was
temporary magnetism, not the attraction of an electrified body for
light bodies, he substituted for the iron filings a non-magnetic sub-
stance, and the phenomenon did not take place. On placing needles

JV^A^V-^.^ ^ Jir^^^A^A^^^ „

FIG. 421.— Magnetization of a steel needle by a solenoid; right-handed and left-handed spirals.

of soft iron, and then of tempered steel, very near the copper wire, he
noticed that the action of the current transformed them into magnetic
needles, having their southern pole always to the left of the current ;
this result agreed with the then recent experiments of Oersted. Soon
after, Arago and Ampere noticed that the magnetism of soft iron, or
that of steel, was developed with much greater intensity by placing
the needle in the interior of an electrical helix. The rheophore wire
of a pile was coiled round a glass tube ; then, having placed in the
axis of the latter the needle to be magnetized, they passed the current
through the wire : magnetization was immediately produced, but, as
might have been expected, it was temporary in soft iron, and
permanent in steel.

Glancing at Fig. 421, we see that there are two ways of coiling
the wire round the tube. Supposing the tube to be horizontal, the

616 PHYSICAL PHENOMENA. [BOOK vi.

wire can be coiled from right to left, each round being coiled from top
to bottom on the side of the tube turned towards the operator ; this
is the right-handed solenoid; or, again, the wire may be coiled
in the same way, but passing from left to right; this is the
left-handed solenoid. If the current traverses the coils of the
spiral from left to right, as indicated by the arrows, the magnetiza-
tion will give a southern pole as to the needle, to the left in the
right-handed spiral ; the southern pole will, on the contrary, be to
the right in the needle of the left-handed spiral.

In both cases, the southern pole is always to the left of the current,
according to Ampere's law.

By this process of magnetization, so simple and wonderful,
secondary poles can be produced at will on bars to be magnetized,
which are called, as we have before seen, consequent points. To
effect this it is sufficient, after having coiled the wire in one direction
round the tube, to coil it in the opposite direction at each of the
points when we desire to produce a secondary pole. The whole

FIG. 422. — Magnetization by a spiral ; production of consequent points.

spiral is thus formed of a right-handed spiral, followed by a left-
handed spiral, and so on (Fig. 422).

We have mentioned that soft iron, surrounded by a magnetized
spiral, assumes temporary magnetism. The magnetic force thus de-
veloped is more powerful according as the iron is more homogeneous
and pure, and as the number of the coils of the spiral is greater. To
realize this last condition, the metallic wire is surrounded by an
insulating envelope, as in Schweigger's multiplier for example, by a
silk thread : it is then coiled round a piece of soft iron, drawing
the coils as close as possible, in order to get a great number of
rounds. It then becomes what is called an electro-magnet; that is
to say, a magnet whose magnetic power subsists during the passage
of the current of the pile, and ceases when the current is discon-
tinued. The form of a cylinder, bent like a horse-shoe, is usually
given to electro-magnets, each branch of \\hich is covered with a

CHAP. V.]

ELECTRO-MAGNETISM.

617

portion of wire (Fig. 423). The spirals here appear coiled in
an opposite direction, but the direction of the coiling is in
reality the same in both branches, if we suppose the cylinder of

FIG. 423. — Horse-shoe electro-magnet.

FIG. 424.— Electro-magnet.

soft iron straightened. We have then at the two extremities, as
soon as the current passes, two poles of contrary names. Electro-
magnets are also made with two parallel iron cylinders of soft
iron, united on one side by an iron plate, and on the other by a

FIG. 425.— Electro-magnet with its charge.

copper plate (Fig. 424). The power of an electro-magnet depends
not only on the number of coils of the conducting wire of the
current, but also on the intensity of the latter, and the dimensions

3 B

G18

PHYSICAL PHENOMENA.

[BOOK vi.

of the soft iron which forms it. The electro-magnet constructed
by M. Pouillet for the Facuite des Sciences of Paris, is capable
of supporting a weight of several thousand kilogrammes.

Many curious experiments can be made with electro-magnets;
we may, for example, form" a magnetic chain, by placing a heap of
magnetic substances, iron filings, nails, &c. below the poles. As soon
as the current passes, the little bodies are attracted by the poles,
which magnetize them by induction, and then get mixed together,
as seen in Fig. 426. As soon as the circuit is broken, all the frag-
ments of the chain fall simultaneously.

FIG. 426. — Magnetic chain.

The promptitude with which soft iron is magnetized under the
influence of electricity, and loses its magnetism as soon as the current
ceases, has brought to light numerous and important applications of
the electro-magnet. We shall see, moreover, that this property has
been utilized in the construction of motive machines, — not very
powerful, it is true, but valuable for work which requires precision
and regularity. In the electric telegraph especially, the electro-magnet
acts this important part, proving how well speculations of the most

CHAP. v.J ELECTRO-MAGNETISM. 619

profound theories lead to practical applications of the highest social
utility. Hereafter we shall do justice to the inventors of the system
who have effected this almost instantaneous mode of communica-
tion of thought ; bub the names of Volta, Ampere, Oersted, and Arago
must be held up to the gaze of the civilized world ; for it is these
celebrated men who discovered the principles which have rendered
this wonderful invention possible.

fi20 PHYSICAL PHENOMENA. [BOOK vi.

CHAPTER VI.

PHENOMENA OF INDUCTION.

Discovery of induction by Faraday — Induction by a current ; inducing coil and
induced coll — Induction by a magnet — Machines founded on the production of
induced currents — Clarke's machine — Kuhmkorff's machine — Commutator —
Effects of the induction coil.

FARADAY, one of the greatest physicists of our century, in
November 1831 discovered a remarkable fact connected with
the electric current ; he found that when a current passes through a
metallic wire, it produces in a second wire, placed parallel to the
first and separated from it by an insulating body, a current which
flows in a contrary direction to the first current. The existence of
the current thus developed by the influence of induction can be proved
by the spontaneous deviation undergone by the needle of a galvano-
meter with which the wire communicates. The second current
quickly ceases, although the first current continues to circulate in
the principal wire ; but if the latter is broken another instantaneous
current is produced in a contrary direction in the parallel wire,
and again ceases immediately. The original current is called the
inducing current ; the current produced when this latter commences
is the inverse induced current ; and, lastly, the current which is de-
veloped when the induction current is stopped, is called the direct
induced current. •

Magnets, as well as voltaic currents, produce induction currents ;
and the same thing occurs with static electrical discharges, as M.
Masson proved in 1834.

To obtain powerful induced currents a considerable length must
be given to the parallel wires. The inconvenience which results from

CHAP. VI.]

PHENOMENA OF INDUCTION.

621

this is avoided by winding each of the wires covered with silk round
a hollow cylinder of cardboard or wood. This is called a coil. The
two extremities of each wire are terminated by two metallic but-
tons, or binding screws, fixed on one of the bases of the cylinder :
these are for the purpose of placing the coil in communication
either with the two rheophores of a pile/ or with a galvanometer.
If we take two coils, one of greater diameter than the other, so
that the smaller can pass within the cylindrical cavity of the
larger one, and place the larger, or induced, or secondary coil in
communication with a galvanometer, and the other, the inducing coil,
into the first ; and if now the latter is placed in communication with
the poles of a Bunsen element, we observe that, so soon as the current
is closed, the needle of the galvanometer is deviated, because an inverse

FIG. 427. — Induction by a current.

induced current has traversed the wire of the first coil ; but the
needle soon returns to zero after slight oscillations, and remains there
se long as the current passes. If the induction circuit is now broken,
the needle deviates in a reverse direction, consequently indicating
the presence of a direct induced current. Then it again returns to
zero and stops there until the current is broken. The same experi-
ment may be made in another manner.

Let us suppose two copper wires wound on the same coil,
well insulated from each other by the silk by which they are
covered (Fig. 427) : the one communicates by its extremities with
a galvanometer G ; the other with the element p of a Bunsen battery.
The current which traverses the coil can be interrupted or established
at will by raising portions of the wire which are immersed in the

622

PHYSICAL PHENOMENA.

[BOOK vi.

vessels g and /, filled with mercury. Now, it is easy to prove,
by observing the direction of the deflection of the galvanometer,
the presence of induced currents, direct and inverse, at the moment
when the inducing current commences and ends.

The first experiment proves that every voltaic current develops,
at the moment of its commencement, an inverse current in the wire
near to it ; and at the moment when it ends a direct current ; so that
its inducing action is nil during the whole time the induction current
is passing.

Let the induction coil be in connection with the pile, and the
circuit closed before the two coils are brought together, as in Fig. 428 ;
if now the inducing and induced coils are quickly brought near each

FIG. 428. — Induction by the approach of a current.

other, an inverse current is produced in the latter, as the deflection of
the galvanometer needle indicates. This current quickly ceases ; but
if then the induction coil is removed, a direct induced current is
developed, and ceases immediately like the first. In a word, every-
thing occurs as in the first experiment.

If the intensity of the inducing current is increased in the
interval which separates the production of the two opposite induced
currents, at the moment when this increase takes place the needle
of the galvanometer, which had returned to zero, is deflected,
and indicates the presence of an inverse induced current. If the
intensity of the current, on the contrary, diminishes, it produces a
direct current in the induced coil.

CHAP. VI.]

PHENOMENA OF INDUCTION.

623

The phenomena of induction by a current may be summed up in
the following statements : —

A voltaic current develops, by influence or induction, in a neigh-
bouring inducing wire, a current of opposite direction to its own,
that is to say an inverse induced current, whenever —

1st. It commences ;

2nd. It approaches ;

3rd. It increases in intensity.

The same current produces a direct induced current, of the same
direction with its own, whenever —

1st. It finishes;

2nd. It recedes ;

3rd. It diminishes in intensity.

We shall now see that the same phenomena are produced with
magnetic currents, that is to say with magnets, and Ampere's theory
thus received from Faraday's experiments a fresh confirmation.

Let us again take a coil, having its extremities in communication
with a galvanometer, and let us place a magnet in the axis of the
cylinder and quickly approach one of its
poles to the coil : the needle of the gal-
vanometer is immediately deflected and
then it returns to zero. The direction of
the deviation indicates a current opposite to
that which, according to Ampere's theory,
represents the action of the adjacent pole of
the coil; moreover, the induced current soon
ceases, and nothing more is manifested so
long as the magnet remains present (Fig.
429). If it is removed suddenly, however,
the needle of the galvanometer is deflected
in a contrary direction, and then returns to
zero after a few oscillations ; it has thus showed the presence of a
direct induced current.

Before approaching the magnet let us suppose that a cylinder
of soft iron has been introduced into the coil (Fig. 430). If now one
of the poles of the magnet is brought near, in the direction of the
axis of the cylinder, induction and the production of an inverse
current will take place for two reasons; first, the presence of the

FIG. 429.— Induction by a magnet.

624

PHYSICAL PHENOMENA.

[BOOK vi.

magnet suffices to produce the induced current ; secondly, the soft
iron is itself magnetized "by induction, and reacts on the coil. This
is proved by the fact that the deviation of the needle of the galvano-
meter is stronger than in the preceding experiment. The same
remark applies to the direct induced current, which the rapid
removal of the magnet develops in the coil. Lastly, if -the distance
of the magnet from the soft iron is varied, the magnetism of this latter
increases or diminishes, and the presence of contrary induced currents

FIG. 430. — Induction by the approach or removal of a magnetic pole.

is proved under both conditions. To sum up, an inverse current of
electricity is induced in a conducting wire by a magnet, whenever—

1st. The magnetic pole is approached ;

2nd. It comes in contact ;

3rd. Its intensity is increased.

On the other hand, a direct induced current is produced
whenever —

1st. The magnetic pole is taken away;

2nd. It is detached ;

3rd. Its intensity diminishes.

The magnetic power of the terrestrial globe, like a magnet,
develops induction currents, and the same thing occurs in the
case of static electrical discharges.

Induced currents are distinguished from ordinary currents pro-
duced by a single pile by their tension, which is much more consider-

CHAP. VI.]

PHENOMENA OF INDUCTION.

625

able than that of the inducing current. They have been utilized in
the construction of electro-motive apparatus of great power. We
may mention Clarke's machine and the coil, the invention of which
is due to M. Masson, but which, having received important addi-
tions from M. Euhmkorff, now bears the name of that celebrated
instrument-maker.

Clarke's machine is represented in Fig. 431 ; it consists of a
powerful magnet, AB, composed of several plates in the form of a

FIG. 431. — Clarke's magneto-electric machine.

horse-shoe solidly fixed to a vertical piece of wood, in such a manner
that its two poles are brought opposite to two coils, each furnished
with a cylinder of soft iron.

The two soft-iron cores are connected on the side of the magnet
by a copper plate, and on the opposite side by an iron plate, t tf ; the
two coils thus arranged constitute in fact an electro-magnet. They
are arranged so as to revolve round a horizontal axis,/, which passes

626 PHYSICAL PHENOMENA. [BOOK vi.

between the arms of the magnet, and is connected behind the
vertical plate with an endless chain and wheel with a handle.

When the machine is put in motion, the two coils turn round
their common axis, and each of them is presented at each revolution
to the poles of the fixed magnet, A B. As the wires of which the coils
are formed are wound in contrary directions, one of them being
left-handed and the other right-handed, it follows that the induced
currents, developed in each of them by the approach of the two
contrary poles of the fixed magnet, are in the same direction. The
direction of these currents changes when the coils get further from
the two poles ; but it changes in both of them at the same time, so
that, at each instant, the induced currents are both direct or both
reversed. The magnetism of the soft iron moreover produces
currents which increase the intensity of the inductive action.
The two wires of the coil terminate at a special apparatus called
a commutator, which is used at will, either to preserve the current
in the same direction during the whole of the movement, or to allow
the direction of this current to change alternately at each half
revolution.

With Clarke's machine all the effects of ordinary electro-motors
are produced, but at a much greater degree of tension than that
produced by piles. Special arrangements permit the production,
sometimes of violent shocks, sometimes of sparks or heating effects,
and sometimes of chemical decompositions. In the last case, the
current remains practically constant ; in the others, on the contrary,
the current must be alternately closed and broken.

Euhmkorff's induction machine is represented in Fig. 432. It
is composed of two coils : the interior one, formed of wire of a
diameter of about 2 or 3 millimetres but of small length, 50 or 60
metres for instance, is the inducing coil ; the two extremities of the
conducting wire terminate at / and /' in two little brass binding
screws.

The induced or secondary coil surrounds the first, which is placed
concentrically in its cavity ; it is formed of an extremely fine wire,
about a quarter of a millimetre diameter, and a length of sometimes
30 kilometres. The two extremities of the induced wire are attached
at the outside to two metallic binding screws, A and B, which are at

CHAP. VI.]

PHENOMENA OF INDUCTION.

627

the top of two insulating glass columns. Lastly, in the interior of
the inducing or primary coil a cylindrical bundle of thick soft- iron
wires is placed, terminated at the extremities by two discs of the
same metaL

Whenever the current of an electro -magnetic machine or voltaic
pile is sent through the inducing wire and traverses it, entering at /
and coming out at/', an induced current will be generated in the wire
of the outer coil, under the double influence of the inducing coil and
the magnetism of the bundle of soft iron. Whenever the inducing
current is interrupted, it will produce in the induced coil a fresh
current of contrary direction to the first. Multiplying the number of
the passages of the current and its interruptions, a series of instan-

FIG. 432.— Ruhmkorirs induction coll.

taneous currents will be produced, so near together and so intense
that the resulting effect will be superior to that of the most powerful
batteries. It remains for us to state by what mechanism these suc-
cessive interruptions are obtained.

At L we observe, mounted on a metallic column, a metal lever
having two branches, one of which has a point on a level with the
surface of the mercury contained in a glass, M, whilst the other
is terminated by a piece of soft iron, reaching to within a short
distance of the bundle of iron wires of the induction coil. When
the point touches the surface of the mercury, the piece of iron
of the other branch is no longer in contact with the iron core,

628 PHYSICAL PHENOMENA. [BOOK vi.

and the reverse of this occurs when this latter contact takes
p]ace — the point no longer touches the mercury. Let us start
from the first position and notice what happens in the apparatus.
The current of the pile then passes through the column which
carries the glass filled with mercury, follows the liquid, the point
in contact with it, and the branch L of the lever descends along the
column which supports it, and by means of a metallic band enters
the wire/' of the induction coil. The current then passes through
the induction coil, returns by / and passes to the other rheophore
of the pile ; thus the contact of the point with the mercury allows
the induction current to pass. But directly this current enters
the coil, the bundle of soft iron is magnetized, attracts the small
mass of the lever, whence results the raising up of the branch
carrying the point ; this leaves the surface of the mercuryj and the
current is broken. Then the magnetism of the bundle ceases, the
contact of the piece of soft iron no longer exists ; and the point
again touches the mercury. The same phenomena are produced in
the same manner as long as the induction coil is in communica-
tion with the pilo. The mercury contact-breaker which we have
just described 'was invented by M. Leon Foucault. Other contact-
breakers produce the same effect by means of a spring.

We have said nothing at present about the commutator, c, the
object of which is either to change the direction of the induction
current, or to interrupt it. Ruhmkorff's commutator (Fig. 433)
fulfils both functions at will : it is both rlieotome (interrupter of
the current) and rhcotrope (inverter of the current). It consists
of a cylinder of wood or glass, the convex surface of which is partly
covered with two copper plates, c c', thick in the middle and thinner
at the edges. These plates have intervening between them two por-
tions of the surface of the insulating cylinder; on each side two
springs, //', press laterally against the cylinder, when it is turned
so as to bring the thickness of the copper plates in contact with
the springs. If, by the use of a milled-head or a handle with which
its axis is furnished, the cylinder is turned through 90 degrees, the
plates of the springs are opposite the glass or wood, which they need
not necessarily touch. In the first position the current passes ; in the
second, it is interrupted. Indeed, the current reaches the pile with
the binding screw A ; thence, by the spring / it passes to the copper

CHAP. VI.]

PHENOMENA OF INDUCTION.

629

plate c. This communicates by a screw g with one of the pivots of
the cylinder, then with the button D, and traverses the circuit, one
of the ends of which is fixed to this latter point. It returns by the
other extremity to the button D' to the second pivot of the cylinder,
and by the screw (f to the plate c', and lastly, by the spring /', to
the binding screw A7, whence it returns to the pile. When the
springs //' no longer touch the plates C c', the current can no longer
pass. This apparatus is then a good interrupter or rheotome.

But when the current passes as we have just stated, it is
sufficient to turn the button through 180°, to change its direction.
For then, the "^te c' touches the
spring/, and the current passes from
D' to D, instead of going from D to D'.
Thus the little apparatus of Buhmkorff
is also a commutator, that is to say, an
inverter of the current, or rheotrope. It
forms part of the induction coil ; but
it is clear that it can be used when-
ever we require to change the direction
of a current.

When EuhmkorfTs coil is at work,
if the two extremities of the wire of
the induced or secondary coil are
brought sufficiently near, a series of
sparks succeed each other with such
rapidity that the line of light appears
continuous. It is remarkable that, of

the two induced Currents Opposite in FIG. 433.— Commutator of Ruhmkorff a

x machine. Plan and elevation.

direction which are generated by suc-
cessive interruptions of the inducing current, the direct current
alone produces sparks; the tension of the inverse current is not
sufficiently strong to allow it to traverse the air.

With the first coils, the length of the sparks attained a maxi-
mum of 8 millimetres. By degrees, improvements — among which
we must point out that of M. Fizeau, which consists in interposing
a condenser, a Leyden jar for example, in the circuit— have led to
the production of sparks from 10 to 20 and 30 centimetres. By

630 PHYSICAL PHENOMENA. [BOOR vi.

increasing the length of wire of the induction coil to 100,000 metres,
M. Euhmkorff was able to obtain sparks of 50 centimetres in length:
blocks of glass four inches in thickness have been pierced through
and through by the discharge. The physical effects obtained with
this powerful machine are extremely remarkable : we may employ
it to charge Ley den jars and electrical batteries. It is thus that
M. Jamin, having charged a battery of 120 Leyden jars with four
coupled coils, each furnished with two of Bunsen's elements, was
able to melt and volatilize iron, silver, and copper wires, more than
a yard in length.

CHAP, vii.] THE ELECTRIC LIGHT. 631

UNIVERSITY

CHAPTER VII.

THE ELECTRIC LIGHT.

BETWEEN the feeble sparks seen in the darkness, when the finger
is brought near a rod of resin which has been rubbed with a
piece of cloth, and the long and bright flashes of fire which are emitted
by the conductors of powerful batteries, or by the dazzling light of
the voltaic arc, there is indeed a difference : it is, nevertheless, the
same phenomenon. It is also the same light which appears with
greater beauty and grandeur in thunder-storms.

Let us inquire into the circumstances under which this light is
produced. We have seen that, whenever two bodies charged with
opposite electricities, at a sufficiently great tension, are near together,
with a non-conducting interval, — that is, when a resisting medium is
interposed between the two bodies, — a spark passes. The tendency
which contrary electricities possess to unite and constitute a neutral
electricity, when they find themselves prevented by the resistance
of a non-conducting medium, leads to this transformation of the
forces, a transformation of electricity into light and heat. Hence
the spark in all its forms.

These varied appearances we shall now review, in the case of
the discharges of static electricity and of electricity at high tension,
and in dynamic electrical currents, which the voltaic pile and induc-
tion apparatus have developed to so high a degree of power.

With ordinary electrical machines of large dimensions remarkable

632 PHYSICAL PHENOMENA. [BOOK vi.

luminous effects may be produced. For tins purpose a metallic plate
is employed, which is held in the hand by an insulating handle, and
is joined by means of a metallic chain to the friction cushions.

By bringing the edge of the plate of the conductor of the machine
to different distances, the spark will at first be seen under the form
of a rectilinear line of light, of a dazzling whiteness and brightness.
If the tension of the conductor is increased by turning the handle of
the machine without interruption, the sparks succeed each other with
so much rapidity that the line of light appears continuous. The spark;
get thinner at their centre, in proportion as the distance of the two
conducting bodies increases, and the rapidity of their succession
diminishes ; then their rectilinear form gives place to lines more or

FIG. 434. — Sparks obtained by the discharge of static electricity.

less zigzag, or serpent-like in form, as if the resistance which the flow
of the electricity undergoes in its passage was unequally distributed.

Besides the principal line of light, we perceive, when the dis-
tance becomes still greater, luminous branches which issue on all
sides, and give to the sparks the forms represented in the drawings
of Fig. 435. These long branch sparks are evidently the form of
transition between the rectilinear spark and the luminous brushes. To
obtain this last form of electrical light produced from the conductors
of ordinary machines, the metallic plate must be presented at a much
greater distance than when the sparks we have first described pass
from the conductor. Then there appears to escape from the conductor
a kind of luminous tree which touches the conductor with its trunk,

b C

CHAP. VIT.] THE ELECTRIC LIGHT. 635

while an infinite number of branches diverges towards the plate.
Fig. 436 shows a luminous tuft as obtained by Van Marum. Between
the plate and the brush there sometimes exists a dark space ; some-
times a mass of light, very narrow, and having its base on the edge of

FIG. 436.— Electrical brush, according to Van Marum.

the plate, joins the top of the brush. In this case we suppose that
the conductors charged with positive electricity, and the plate elec-
trified by induction is therefore charged with negative electricity. If
the reverse took place, the brush with wide ramifications would escape

3 c 2

636

PHYSICAL PHENOMENA.

[BOOK vi.

FIG. 437 —Positive and negative brushes.

from the plate and the narrow root from the conductor. Faraday,
who studied the forms of positive and negative brushes, showed
that this difference results from an unequal tension of the two
electricities when the discharge
takes place. Negative electri-
city requires for its discharge
a much lower tension than posi-
tive electricity.

The electric light can be
produced in different media,
in air and other gases, and
even in bad-conducting liquids:
its appearance, that is to say,
its form and colour, changes
according to the nature of these media ; and when the discharges
take place in a gas, they vary with its pressure or degree of rare-
faction. In air, at ordinary pressure, we have seen that the spark

is a brilliant white. According to
Van Marum, who made numerous
experiments on this subject, its
colour is bluish, tinged with purple,
in nitrogen; very white in oxygen;
violet red in hydrogen ; greenish
in carbonic acid ; reddish-green
in carburetted hydrogen gas, and
white in hydrochloric acid.

The trunk of the positive lumi-
nous brushes in air, at the ordinary
pressure, is of a violet colour, tinged
with purple, whilst the branches
are white, — this is perhaps because
the light is less condensed. In
other gases the colour of the brush
varies, as Faraday's experiments
showed : thus, in hydrogen and in

FIG. 438.— Light in the barometric vacuum. coal g3S, it is slightly greenish ; ill

oxygen it is white as in air, but much less beautiful ; in rarefied
nitrogen it is, on the contrary, a magnificent purple ; in carbonic

CHAP. VII.]

THE ELECTRIC LIGHT.

637

oxide and carbonic acid it is greenish in the first gas, and slightly
purple in the second. In the barometric, or Torricellian vacuum,
there is no spark, or rather the spark appears between the conductor
and the metallic wire which dips in the mercury : at this moment
the barometric vacuum is illuminated with a greenish light, as in
Fig. 438.

For the study of the luminous effects produced by electrical
discharges in rarefied gases, the apparatus represented in Fig. 439 is

Fiu. 4a». — i'lie elueiiie egg.

Fio. 440.— Electric light in rarefied air.
Purple bands.

employed: this is called an electric egg. The two metallic rods,
each terminated by a ball, and communicating with the conducting
caps of the apparatus, can be approached or separated at will. The
egg can be detached from its stand and screwed on the plate of an
air-pump, so that the air can be rarefied at will, a vacuum made
and a gas introduced at any pressure.

In air, at ordinary pressure, the spark obtained between the two
balls is similar to that we have described at the beginning ; but in

638 PHYSICAL PHENOMENA. [BOOK vi.

proportion as the air is rarefied, the light changes in appearance and
escapes from the positive ball as a branched sheet ; at a pressure of
60 mm. it presents the appearance shown in Fig. 440. It then appears
to be composed of a number of luminous bands of a purple colour,
some diverging laterally, others terminating at the negative ball,
which is itself enveloped in a thick sheet of violet light. When the
pressure is reduced to a few millimetres, the bands unite into a
luminous sheaf, in the form of a spindle.

The various luminous phenomena we have just described are
produced by static electrical discharges. Between the two approxi-
mated ends of the rheophores of a pile with a very large number of ele-
ments, brilliant sparks may be obtained which succeed each other with
rapidity. We have stated above that the phenomenon is much finer,
and the light more intense, when it is caused to pass between two
carbon points terminating the extremities of the rheophores : we then
obtain what is called the voltaic arc. By making use of induction
currents, extremely remarkable luminous effects may be obtained
without the necessity of a pile with a great number of elements. The
following are some details of the voltaic arc : —

We have already said that, in order to produce the luminous arc,
it is necessary to place the carbon points very near to each other ;
but when once the current has conquered the resistance of the
interposed air and produces the light, the points can be further
separated : Davy, working in rarefied air, obtained with his pile of
2,000 couples an arc of light of seven inches in length. The
luminous intensity of the voltaic arc is so considerable that the
eye can scarcely endure its brightness. According to some ex-
periments made by MM. Fizeau and Foucault, this intensity is
nearly fifty times greater than that of Drummond's light, — that
is, the brilliant light produced by directing an ignited jet of
oxy-hydrogen gas on a piece of lime; solar light has scarcely an
intensity triple that of the voltaic arc. These two experimenters
worked with a Bunsen's battery of 92 couples arranged in two
series.

In studying the very interesting phenomenon of the voltaic arc,
it has been noticed that the electrical current passing continuously
between the two points transports from one to the other minute
particles of carbon : this transport of matter is made with greatest

CHAP. VII.]

THE ELECTRIC LIGHT.

639

readiness from the positive to the negative pole, so that the points
become unequal in size : the negative point increases at the expense
of the other. Fig. 441 shows the appearance of the two points, as
seen by projection on a screen, in an enlarged form. We will leave
the description of it to the learned physicist to whom we owe

FIG. 441. — Carbon points of the electric light and the voltaic arc between them.

this drawing. M. Le Roux, at a lecture on the application
of electricity to lighthouse illumination, given by him at the
Societe cF 'Encouragement pour V Industrie nationale, described it
as follows : — " In order to directly examine what passes in the
voltaic arc, great care must be taken to place the eye in

640 PHYSICAL PHENOMENA. [BOOK vi.

safety from the considerable intensity of the light, but this
same intensity allows us to observe the whole of the smallest
details of the carbon surfaces. It is sufficient to interpose between
them and the screen a lens with a proper focus : you will thsn
perceive the image of the carbon points enlarged a hundred times ;
this projection enables you to examine, without fatigue, the whole
of the phenomena. Here are some carbon points between which
the continuous current of a Bunsen's pile passes. You see one
of the points increases at the expense of the other: this one,
which is the most used, is the positive point ; it is this which
communicates with the carbon end of the pile ; if it is more pointed
than the other, it is because it loses material which the other
acquires. We can, indeed, reverse the direction of the current : you
then see the carbon point which was just noW the most pointed,
increases, whilst the other becomes more slender ; besides, from time
to time some larger patches detach themselves, traverse the space
under the form of little incandescent masses^ and indicate the direc-
tion of transport. You see little globules boil up here and there
on the surface of the carbon ; these are globules of melted silica :
you will remark that these globules do not appear on the carbon
points where the temperature is highest ; they are volatilized at the
outset. Now we are in a very impure vein, and a considerable
quantity of these silica globules show themselves ; the brightness of
the arc suffers; blowing lightly against the carbons, the current of
air inclines the arc and shows us its development. We now reach
a part of the carbons where their purity leaves nothing to be desired.
You see how quiet the arc is, the progress regular, the points clearly
terminated. You will see the quiet, bluish light of the arc contrast-
ing with the bright white of certain parts of the points ; the arc
forms a kind of truncated cone swollen in the middle, the two bases
of which are the carbons: these two bases are the brightest por-
tions, the temperature is the highest in them, the molecules trans-
ported by the current strike them."

When a space filled with gas or very rarefied vapours is
traversed by induction currents, the luminous effect presents par-
ticular characteristics of great interest.

If the air contained in an electrical egg is rarefied to a pressure

CHAP. VI 1.1

THE ELECTRIC LIGHT.

641

of two or three millimetres, and if the interior balls are placed
in communication with the poles of a BuhmkorfFs coil, a magnificent
luminous sheaf is seen, of a beautiful red, starting from the positive
ball, whilst the negative baU and rod are enveloped in a sheet of light
of a bluish purple. If the direction of the current is reversed with
a key, or commutator, the two lights are inverted ; the sheaf issues
from the lower ball, whilst the violet aureole envelopes the upper ball

FIG 442. — Luminous sheaf in rarefied air.
Discharge of induction cuirents.

FIG. «J. -Stratified light in rarefied gas.

If, before rarefying the air, vapours of different substances are intro-
duced,—for example, alcohol, phosphorus, or .essence of turpentine, —
the luminous sheaf assumes a particular aspect which was discovered
nearly at the same time by Ruhmkorff, Grove, and Quet. The red
light of the sheaf is interrupted transversly by very narrow dark
bands, so that it is alternately formed of dark and bright stria?. From
the middle of the sheaf, where the stria? are rectilinear, they are
curved in two opposite directions, each facing the balls concavely.

642 PHYSICAL PHENOMENA. [BOOK vi

To this phenomenon is given the name of stratification of the
electric light.

Since the time of this discovery, different forms have been given
to the vessels which contain the rarefied vapours suitable for the
production of the stratifications. The most curious effects of the kind
are produced in tubes known as Oeisslers tubes. The beauty of these
luminous effects is again enhanced by the phenomena of phosphor-
escence which the electric light produces in uranium glass, and in
certain salts (notably sulphides) of strontium and calcium, and also
in sulphate of quinine.

BOOK VII.

ATMOSPHERIC METEORS,

3 D 2

BOOK VII.

ATMOSPHERIC METEORS.

THE reader who has occupied himself with the studies of which
we have spoken at some length, though in a very incomplete
manner, will find that all the physical phenomena of nature arrange
themselves in one or other of the categories which correspond to the
six Books of this work : Weight, Sound, Light, Heat, Magnetism, and
Electricity. We have seen moreover that electricity and magnetism
have the same cause — that they are, in fact, two modes of action, at
first sight different, but really the same, resulting from the same
physical agent. The more science advances, the more are the divi-
sions of which we speak effaced; in other words, the more evident
does it become that one principle will probably some day or other
account for the varied phenomena perceived by our senses, and of
which the world presents a perpetual development. Moreover, in
nature these phenomena are not isolated: the separation which
science is obliged to make, without which separation indeed science
would not be possible, does not exist in reality ; not only do the
phenomena co-exist, but they act and re-act one on the other; they
strive with, interpenetrate, and modify each other in a thousand
different ways, and these are the innumerable actions which become
to the observer or contemplater of the universe the source of all the
contrasts and of all the harmonies which he observes.

646 PHYSICAL PHENOMENA. [BOOK vn

In this concluding Book it is impossible to present a sketch of
the immense picture — the magnificent panorama which results from
the concourse of physical phenomena ; but we cannot omit showing
the ties by which some of them are bound to the facts which we
have studied, and which the physicist reproduces on a smaller scale
in his laboratory. Let us for this purpose consider some of those
phenomena which are called atmospheric, the place of their produc-
tion being the aerial envelope with which the terrestrial globe is
surrounded. They may be arranged in three principal classes :
luminous or optical meteors / aqueous meteors, the production of which
is due to the modification undergone by aqueous vapour under the
influence of variations of pressure and temperature ; and lastly,
electrical or magnetic meteors.

The refraction of the luminous rays which have to pass through
either the entire strata of the atmosphere, or a part of them, gives
rise to numerous phenomena, amongst which we have already de-
scribed the apparent elevation of objects above their real position,
which is called atmospheric refraction. Mirage is a phenomenon due
to the same cause ; it is observed chiefly on the surface of plains of
sand, when the ground has been strongly heated by the sun's rays.
The traveller who crosses these plains then sees objects which are
raised above the ground, reflected as if on a liquid expanse ; the
illusion is so strong that those who are, for the first time, witnesses of
the phenomenon, cannot help believing in the real existence of a lake
spreading its waters along the horizon. The French soldiers in the
Egyptian expedition were more than once deceived by this false
appearance. Overcome with fatigue and thirst, they saw the longed-
for lake recede as they approached, renewing for them, under a form
not less deceptive, the tortures of Tantalus. Monge, one of the men
of science of the Egyptian Institute, was the first to give a complete
explanation of the mirage, which, however, is not alone observed in
the African deserts.

The following is his theory of the mirage. The solar rays, on
reaching the surface of the sandy stratum, heat it strongly, whilst
they have passed through the superposed strata of air without much
raising their temperature, — the absorbing power of gases being very
small compared with that of solids. But the heat of the ground is

!' I.!,1 ! ||||||l UiU Illll HI "I1 !'••!!,

BOOK vii.] ATMOSPHERIC METEORS. 649

communicated by direct contact to the lowest stratum of air and from
that successively to these above it ; and expanded air rises in virtue
of its specific lightness ; but if the ground presents a nearly horizontal
level, and if the atmosphere is calm, equilibrium is retained, and feeble
currents produced by some inequalities in the expansion of the
different portions of the lower air are alone produced. Hence it
follows that, towards the middle of the day, the strata of the air
nearest the ground are arranged, from top to bottom, in the order of
decreasing density. Let us now imagine a luminous beam sent
obliquely to the ground from the point M, a tree in our sketch
(Fig. 445) ; on passing from the rarer into the denser stratum, it
will deviate from the vertical, from a to d, and this deviation will
increase in proportion as it encounters strata more and more refrac-
tive, until falling at A on a stratum with the surface of which

FIG. 445. — Fxplanation of a mirage.

it makes an angle equal to its limiting angle, it will undergo total
reflection. Starting from this point, it will follow a contrary path,
getting nearer and nearer to the vertical, falling on o in the observer's
eye, who then sees an image of the point M in M'. The same path
being applied to all the points of the object — here it is a tree, — it will
appear reflected as in a mirror, and the observer will see it as a
reversed image. The sky is reflected in the .same manner, whence
the brilliancy of the ground at a certain distance from the object, and
the appearance which causes the belief in the presence 'of a liquid
between the eye and the object.

650 PHYSICAL PHENOMENA. [BOOK

The phenomenon of the mirage takes place also on the surface
of the sea, when the water has a higher temperature than that of
the air, and the explanation is the same as that of the mirage on land.

When the strata of the air are unequally heated, instead of
being separated by horizontal surfaces, they are more or less oblique
and we get the lateral mirage which is observed principally in
mountainous countries, or in the vicinity of buildings : in this last
instance, the objects appear reflected as in a vertical mirror. It even
happens, as is sometimes observed at sea, that the mirage of the
object, as a vessel, for instance, is formed above it. The son of a
celebrated navigator and physicist, Scoresby, witnessed in the polar
seas this last phenomenon, which was then called the inverted mirage.
One day he perceived in the air the inverted image of the ship which
his father commanded, and from which a sudden storm had separated
him, and the image was so clear that he could recognise the vessel,
although it was completely hidden below the horizon. To explain
this phenomenon, the existence of horizontal strata of air, the density
of which rapidly diminishes from below upwards, must be supposed
at a certain height in the atmosphere.

The mirage is a phenomenon of simple refraction. The rainbow ,
halos, and parhelia are luminous meteors produced by the dis-
persion of light during its passage through rain-drops, the very
small drops of which form the clouds or haze which float in the
atmosphere. We shall confine ourselves to a statement of the theory
of the rainbow, propounded by Antonio de Dominis in 1611,
elaborated by Descartes, and lastly perfected by Newton.

We all know that the rainbow or iris is seen opposite to the sun,
" through the clouds which are turned into rain, and that it is some-
times simple and sometimes accompanied by an outer bow less
brilliant than the first. The principal or interior bow forms a
circular band in the width of which the various colours of the
spectrum are seen in order from violet to red, starting from the
inside of the bow. The secondary bow is wider than the first and
shows the same colours arranged in a reverse order, so that the red
is inside, next to the red of the principal bow.

To account for the conditions \\hich produce the phenomenon,
let us trace the path of a solar ray, which falls on the surface of a

YJI.] ATMOSPHERIC METEORS. 651

spherical drop of rain. On arriving at the surface of the sphere, the
luminous ray is refracted and approaches the normal at the point of
incidence. On meeting the interior surface of the liquid sphere it is
divided ; part of it emerges and the other part is reflected. The same

Fio. 446.— Paths of the effective rays through a drop of rain after a single internal -reflection.

effect takes place at each of the meetings of the reflected ray with the
surface of the drop, the intensity of the reflected light diminishing in
proportion as the successive reflections are accomplished. Knowing
the angle of incidence of the luminous ray, the angle at which it

FIG. 447. — rath of the effective rays after two interior reflections.

leaves the liquid sphere, after one, two, or any number of interior
reflections, can be calculated. Instead of a single ray of light, if we
imagine a beam such as s I, the angle of incidence of the rays which
compose the beam, not being the same for all, the emerging rays will

652 PHYSICAL PHENOMENA. FBOOK

emerge generally in diverging from the sphere, in such a manner that
if dispersed through space they could not act on the eye or produce
an image on the retina at any distance. Nevertheless, calculation
proves that for certain incidences the emergent rays form a cylindrical
beam, the intensity of which will remain sensibly the same at a
considerable distance. Newton gave the name of effective rays to
those which possess this property.

Let us recall to mind that the different coloured rays of which a
beam of white light or solar light is composed have not the same re-
frangibility. The incidences which correspond to the effective rays of
each simple colour are therefore not the same ; hence it follows that on
emerging from the liquid sphere the incident beam will be divided
into as many separate rays as there are colours in the spectrum. On
calculating the angles of incidence for the rays of the extreme simple
colours, the violet and the red, after a single internal reflection we find :

For the violet rays, an angle of incidence of 58° 40'; for the red
rays, an angle of incidence of 59° 23'.

Therefore the angles which the emerging rays make with the
direction of the incident rays are 40° 17' for the violet rays, and
42° 2' for the red rays.

In the case of two internal reflections, in A and B, the angles of
incidence of the effective rays are :

For the violet, 71° 26'; for the red, 71° 50'; and the deviations
undergone by the rays, after this emergence from the liquid sphere,
are 50° 59' for the red rays, and 54° 9' for the violet rays.

By means of these data, it may be seen that the principal rainbow
is produced by the solar rays which have undergone a single reflection
in the interior of the liquid spheres composing the rain-drops. The
secondary rainbow is produced by the rays which have passed through
two successive reflections. Let o z be a line parallel to the direction
of the solar rays, and passing through the eye of the observer who
turns his back on the sun. Looking in the direction o «, so that the
angle a o z is that of the deviation corresponding to the effective
violet rays, the observer will receive on his eye a violet ray pro-
ceeding from the solar ray s a, which has been once reflected in the
rain-drops, when they pass successively in their fall by the point a.
Indeed the parallelism of the lines o z and s a conduces to the equality
of the angles Sao and a o z ; now this last is by hypothesis equal to

VII.]

ATMOSPHERIC METEORS.

653

the angle of deviation which corresponds to the effective violet rays.
The ray s a will then find a rain-drop, whose position will be that
which agrees with the calculated incidence and emergence ; and the
observer will see a violet point. About 2 degrees higher, at b, he will
see a red point, and in the interval a b all the shades of the spectrum
comprised between the violet and the red ; that is to say, indigo
blue, green, yellow, and orange. But the same thing will evidently
occur in every direction making with o z the same angles as those of
which we have spoken. The observer will then see bands of all these
colours, projected on the sky under the form of concentric circles

Fio. 448.— Theory of the rainbow ; formation of the principal am] secondary arc.

having their centres on the line o z, in a point diametrically opposite
to the sun. So much for the solar rays which penetrate the rain-
drops and emerge after a single reflection. Those which have under-
gone two reflections will arrive at the eye forming with the line o z
angles of 50° 59' if they are red rays, and 54° 9' if they are violet rays.
The effective rays of the intermediate colours will be comprised
between these extreme rays ; but in this case the red will be at the
inside and the violet at the outside of the arch.

These results are deduced from calculation, according to the

654 PHYSICAL PHENOMENA. [BOOK

laws of reflection and refraction of light, and the index of refraction
of water. Now, the angular dimensions of each rainbow, the
width of the zones, and that of the interval which separates them,
are so many consequences of the preceding data, and, if the theory
is correct, observation ought to verify the truth of it ; and indeed
the explanation given by Newton, and by all observers after him
who have studied the rainbow, has been verified. When the sun is at
the horizon, the line o z is in this plane ; the centre of the arcs is
then itself at the horizon, and the rainbow is seen under the form
of a semicircle ; and it presents this form both at the rising and
the setting of the sun to an observer situated in the plain. For
different heights of the sun, the rainbow has an amplitude less
than a semi-circumference, which gets less as the sun gets higher.
Lastly, if the observer were situated on a very high mountain and
on a narrow peak, he would be able to see more than a semi-circum-
ference, and even a complete circle, if the rain fell at a considerable
distance.

It must not be forgotten that the rainbow is a phenomenon the
production of which depends only on the position of the observer
relatively to that of the sun and of the cloud which is converted
into rain. Therefore if two persons at a distance from each other
see a rainbow at the same time, they do not see the same arc.
If the arc were the same everywhere an observer situated obliquely
would see it in perspective, and in the form of an oval or ellipse,
not as a circle. Theory and observation agree in showing that this
is never and can never be the case. We have often heard persons,
to whom we have mentioned having seen a rainbow, reply that
they had seen the same rainbow; unless they are precisely in the
same position, no two persons ever see the same bow at the same
instant.

Aqueous meteors are those caused by the transformations which
the vapour contained in the air undergoes, under the influence of
variations of temperature. Clouds, fogs, rain, snow, dew, white
frost and hoar frost, are the different forms under which the atmo-
spheric water is presented to our view, which therefore assumes these
three conditions : the gaseous condition, when its exists as invisible
vapour ; the liquid condition, when the lowering of temperature

vii.] ATMOSPHERIC METEORS. 655

condenses it into drops ; lastly, the solid condition, if a still greater
cooling congeals the drops which then fall in the form of white flakes,
or arrange themselves into crystals on the surface of the ground. The
complete description and detailed explanation of these different
phenomena would take US' beyond the limits of our space. We shall
therefore confine ourselves to an indication of the physical laws which
relate to their production.

Analysis proves that the air is a mixture of two permanent gases,
oxygen and nitrogen, with which variable quantities of aqueous
vapour and carbonic acid are mixed. But while the proportion of
oxygen and nitrogen remains constant, that of the aqueous vapour
varies perpetually and depends on numerous atmospheric conditions,
such as temperature, direction and force of the wind, &c.

It is very important to the science of meteorology to know how
to determine, at a given instant, the hygrometric state of the air.
By this term we understand the relation between the tension of
the aqueous vapour, which is actually contained in it, and the
maximum tension which the same vapour would possess if, at an
observed temperature, the air were saturated with it.

This relation is deduced from the indications of instruments
called hygrometers, constructed on different principles, among which
we shall only describe the hair hygrometer, which bears the name of
De Saussure, its inventor.

It is based on the property which hairs, like many other animal
substances, possess, of being very sensible to variations of atmo-
spheric dampness. A hair previously washed in sulphuric ether,
which frees it from the oily matter which it contains, lengthens when
it absorbs aqueous vapour and shortens when it loses the absorbed
moisture. The following is the manner in which these changes of
dimensions are rendered sensible : —

The hair is fixed by its upper extremity, and passes round a
pulley at the centre of which there is a needle moving on a divided
circle. A small weight keeps it on the pulley ; and as this forms with
the needle a system of unstable equilibrium, the least variation in the
length of the hair turns the pulley, and therefore the needle, in one
direction or the other.

The hygrometer is graduated by taking, for the fixed points, the
extreme dryness or dampness of the air, by'the following method : —

656

PHYSICAL PHENOMENA.

[BOOK vii-

The instrument is placed under a bell-jar, the air of which is dried
by chloride of calcium, and when the needle stops at a fixed posi-
tion, it is marked 0°; the apparatus is then placed under another
bell-jar, the interior of which is moistened with water : the air con-
tained in this jar is thus saturated with vapour. The needle passes
in the contrary direction, and ends by stopping at a point which
corresponds to the state of the air saturated with
vapour.

This point is marked 100°, and the interval
comprised between the two fixed points is divided
into 100 equal parts or degrees.

The hygrometer thus constructed and graduated
shows well if the air is more or less damp ; but
to conclude, from a marked hygrometric degree,
the tension of the vapour with regard to the ten-
sion of the air saturated at the same temperature,
one must construct and calculate empirical tables
which give this relation. A thermometer is
generally added to a hair hygrometer, the utility
of which will be understood after what we have
just said. Hair hygrometers present this incon-
venience, that their indications are not exactly
comparable; hairs belonging to different indi-
viduals have not in the same degree the pro-
perty of absorbing dampness.

The hygrometric state of the air can also be deduced from the
temperature to which it must be lowered, in order that the vapour
which it retains may be sufficient to saturate it. The instruments
which serve to determine this temperature are condensing hygro-
meters, thus named because the vapour condensed on the surface
of a polished metal indicates the saturation of the air produced by
an artificial falling of the temperature : these instruments are pre
ferred by meteorologists on account of their precision. The quantity
of atmospheric aqueous vapour generally increases with the tempera-
ture ; it is greater at sea and on the coast than far inland. It varies
according to the hours of the day, increasing in proportion as the
temperature rises. . It also varies in the various seasons of the year;
the warmest are those in which the air contains the greatest absolute

FIG. 449. — De Saussure's
hair hygrometer.

FIG. 4 JO.— Forms of snow crystals (Scorosby).
3 K

BOOK vii.] ATMOSPHERIC METEORS. 659

quantity of vapour. The contrary, however, happens for relative damp-
ness ; it is generally during the night, or during the cold season, that
it exists in greatest quantity, — that is to say, that the air is nearest
saturation. Lastly, the direction of the wind has also a great
influence on the hygrometric condition of the air, but it is impossible
to give an idea of this influence without entering into extremely
complex details, since the atmospheric conditions change, so to speak,
in different regions of the globe.

Dew is nothing more than a deposition of the vapour contained
in the air, which the cooling of objects situated on the surface of
the ground has condensed into fine drops during the night. Dew
appears especially during the serene nights of autumn and spring :
because, at these periods, there is a great difference between the warm
temperature of the day and that of the night. The atmosphere then
contains, during the day, a sufficient quantity of vapour ; and, if the
sky is not covered with clouds, the ground radiates into space a
quantity of heat, without the air in itself being cooled as much in its
upper strata : but the contact of the ground will cause the tem-
perature of the lower strata to fall. As these contain a good deal
of vapour, the point of saturation will soon be reached, and their
vapour will be deposited in the form of dew on bodies, the more
freely, the worse conductors of heat and the better radiators the
bodies are.

Clouds prevent radiation from being so intense ; and, moreover,
between them and the ground an exchange of heat takes place : this
explains why there is little or no dew in dull weather.

When the temperature of the night falls below freezing-point,
the dew deposited on the ground is congealed, crystallizing in the
form of very fine icicles : this phenomenon is known as white or
hoar frost.

When the condensation of the atmospheric vapour is determined
by a fall of temperature in the upper strata of air, very small drops
of water produced by this condensation, collected in a space more
or less great, interfere with the transparency of the air, and form
either clouds or fogs. Fogs differ from clouds only by their proximity
to the ground. Clouds continually change in form ; but it is not
alone the influence of aerial currents which modify them : sometimes

3 E 2

660

PHYSICAL PHENOMENA.

[BOOK

they are dissipated, because they meet -with strata of a higher tem-
perature, and part of the water which forms them passes into the
state of vapour; sometimes, on the other hand, they increase by
a fresh condensation, and then, if the drops assume a more consider-
able volume and weight, they fall to the ground as rain. A change
of wind often brings rain, either because the cold masses of air are
thus mixed with air charged with vapours, and, reducing its tem-
perature, bring it to saturation point ; or, on the other hand, because
the masses of warm air charged with vapour are then mixed with
a colder atmosphere.

In winter, when the temperature is low enough for the drops of
water, forming clouds, to be congealed, snow falls intead of rain.
Snow-flakes are formed by the agglomeration of small crystals,

FIG. 451. — Dissection of a block of ice by the solar rays. Crystalline structure of ice.

deposited in a star-like form, with a symmetry which is really
wonderful. We have reproduced in Fig. 450 the various forms
which the navigator Scoresby has described, and figured in the
account of his voyages to the Arctic seas. It has been remarked
that the greatest number of them are hexagonal polygons — stars
With six points ; all the small facets forming the crystals making
angles of 60° or 120°. Sometimes drops of water from the clouds
are agglomerated, on congealing, into little irregular masses more
compact than snow. They then fall as sleet, or hail.

The crystalline form assumed by atmospheric water on congealing
also belongs to the compact and transparent masses of ice which the
low temperatures of winter produce on the surface of ponds, lakes,
and rivers. On examining ice with the naked eye, its structure
appears confused, but Tyndall has succeeded in proving its crystalline

VII.]

ATMOSPHERIC METEORS.

661

texture by a very curious experiment, which consists in passing a
beam of solar or electric light through a block of ice. The heat of
the beam is partly absorbed by the molecules of which the block is
composed, and the return to the liquid state is gradually produced.

Fio. 452.— Ice-flowers (Tyndall)

By examining what is passing in the interior of the block by
means of a magnifying-glass, or by projecting its image on a screen
by means of a lens, the work of decomposition of which we speak
is rendered evident. Here and there we see star-flowers with six
rays, with serrated edges ; at the centre of each a spot is seen present-
ing the lustre of burnished silver, and Tyndall has shown that this

662

PHYSICAL PHENOMENA.

[BOOK

spot is a vacuum, the production of which is due to the diminution
of volume undergone by the ice as it passes to the liquid condition,
so that this curious phenomenon proves the contraction of water
during its passage from the solid to the liquid state.

The various phenomena we have just rapidly described, and
which we have placed under the common denomination of aqueous
meteors, because water in its different states forms the substratum
of them all, have for their cause the variations of temperature.
This last element has therefore great importance in meteorology;
moreover its influence is very great on organized and living beings,
both animal and vegetable, on their production and development, —
in a word, on the life on the surface of the globe ; it acts in such a
continuous manner on the health of man and his auxiliaries, that the
problem which consists in determining its variations, periodicity, and
anomalies, is surely one of the most interesting in meteorological

! "£ J

-j - — *| ,.!

FIG. 453. — Rutherford's maximum and minimum thermometers.

science. But its complexity is such, that it is not possible to touch
upon it here or even to glance at it ; we shall content ourselves with
describing the instruments used in the observation of the temperature
of the air. We already know the nature of the different kinds of
thermometers used for this purpose : it only remains for us to speak
of the form given to them, when we desire to know the highest
or lowest temperature which the air has attained during a certain
interval of time. These are termed maximum and minimum ther-
mometers.

Fig. 453 represents an instrument of this kind invented by
Rutherford ; it consists of two thermometers, one of mercury and
the other of alcohol, placed horizontally on a wooden frame. In the
interior of the first tube, a little cylinder of steel or enamel is in
contact with the surface of the mercury, which the liquid forces before

VII.]

ATMOSPHERIC METEORS.

663

it as long as the temperature rises ; but which it leaves in its place,
at the most distant point of its course, when the temperature falls-
The end nearest the mercury evidently indicates the maximum tem-
perature. In the tube of the alcohol thermometer is an enamel
cylinder which the alcohol moistens and leaves in its place when
the temperature rises, and which it draws with it when it falls.
The minimum is then given by the end of the cylinder furthest
away from the reservoir. When the instrument is adjusted for an
observation, care must be taken to bring the two indices to the
extremities of each liquid column ; one is in contact with the
mercury, and the other is immersed in the alcohol, the end most
distant from the reservoir being on a level with the surface of the
liquid.

To observe maximum and minimum temperatures at great depths,
in the sea, or lakes, or Artesian wells, upright thermometers are
used, among which we may describe those of
M. Walferdin.

The maximum thermometer is constructed like
a common mercurial thermometer ; but the ex-
tremity of the tube is brought to a point, and con-
nected with a lateral reservoir which contains a
certain quantity of mercury. When an observation
is to be made, the reservoir is heated until the mer-
cury entirely fills the tube, then the instrument
is reversed, the reservoir being uppermost ; the
mercury in the lateral reservoir is now on a level
with the point, and on cooling to a lower tempera-
ture than that of the maximum to be determined
the tube remains always filled with mercury.
The instrument, thus prepared, is placed in the
medium to be observed. As long as the tem-
perature rises, the mercury flows into the reservoir,
and at the moment of the maximum the tube will
be still filled. The instrument being removed from

0 .

the medium and reversed, the maximum tempe-
rature will be found by heating the thermometer in water until the
column of mercury is again on a level with the passage leading into
the lateral reservoir.

minimum thermometers

of M Wulferdin.

664 PHYSICAL PHENOMENA. [BOOK

For meteorological observation, self-registering thermometers are
now constructed which mark all variations of the temperature by
means of photography, the exact time of observation being determined
by interruptions of the record at known intervals.

The variations of atmospheric pressure are not less valuable
for the knowledge of meteorological laws than those of temperature ;
we will say a few words on this subject before describing electrical
and magnetical meteors.

In Chapter VIII. of Book I. we have seen how barometers show,
by variations in the level of a column of mercury, the corresponding
variations of the pressure of the atmosphere. These oscillations
of the barometric column have very complex accidental causes. If
the atmospheric column which rests upon any certain surface were
always at rest, the pressure would only depend on the weight of
air of which this column is composed, to which must be added
the pressure resulting from the elasticity of the vapour which
is mixed with it ; but this state of equilibrium never exists on
any part of the globe. The reasons for it are easily understood,
and, moreover, proceed more or less directly from the same cause ;
namely, the action of solar heat.

The sun warms the surface of the ground and the strata of super-
posed air in any place very unequally, according to the hour of the
day and the time of the year. The more considerable this heating
action is, the more is the air expanded, and the more readily does
it rise by diminution of density. But as, at the same instant,
the regions more or less distant from the first are in different
conditions, there ceases to be equilibrium : then the highest strata
of air pass from the warmest region towards the coldest, and a
movement in a contrary direction takes place below, — that is, a
passing of the denser and colder strata of air towards the warm
region. This transport of masses of air from one place to another
is the cause of winds. Now, it is clear that at the commence-
ment of this movement a diminution in the barometric pressure
will be produced when the air has been expanded by the eleva-
tion of temperature; then also an augmentation will result when
the temperature is lower, the weight of the air being increased
by the whole weight of the strata which are spread out 011 the

vii.] ATMOSPHERIC METEORS. 665

upper surface of the atmosphere. But it must not be forgotten that
the heating action of the sun produces at the same time a contrary
effect. The vapour contained in the air increases its elasticity
as the temperature rises, so that if the barometric column falls
when the density of the air diminishes, at the same time it rises
under the influence of the increase of tension of the aqueous vapour.
The difference of these two contrary movements produces the
barometric variation.

Lastly, it is probable that atmospheric currents act in another
manner on the column of mercury of the barometer. For instance,
if an aerial current is propagated from above downwards, its
influence will depend not only on its weight, but also on the
velocity with which the gaseous mass will be moved, just as if,
as M. Marie'-Davy has well said, the winds have for their original
cause a difference of pressure occasioned by the inequalities of
temperature ; they react on themselves, producing variations of
pressure. It has been noticed, that, at the same place, the baro-
metric column undergoes diurnal oscillations and variations which
follow the seasons of the year: both are subjected to a periodicity
which agrees with the preceding explanations. But this same
height is subjected to irregular variations, the causes of which
are extremely complex.

Thus, the barometer rises or falls according to the direction of
the prevailing wind. At Paris and over a great portion of Europe,
the barometric pressure is generally higher with the north, north-
east, and east wind than with the south, south-east, or south-west
wind. In the southern hemisphere, the contrary takes place.

We will conclude this explanation of the causes which produce
the principal atmospheric phenomena, by a short description of
electric and magnetic meteors.

In 1735, Gray pointed out the analogy which exists between
lightning and the noise of thunder during storms, and the spark
and sharp sound produced by an electrical discharge. But it is to
Franklin that the honour belongs of having established by decisive
experiments the identity of the causes of these two phenomena.
In 1749, this illustrious physicist, after having noticed all the
similarities between thunder and electricity, which had been hinted

666 PHYSICAL PHENOMENA. [BOOK

at by preceding observers, conceived the possibility of utilizing
the power of points to preserve edifices from lightning. At the
same time he gave all the indications necessary for detecting by
experiment the electrization of thunder-clouds. Three years later,
he used a . kite surmounted by a metallic point to draw sparks
from the string wetted by the rain. Nearly at the same time
Dalibard realized, in his celebrated experiment at Marly-la- Ville,
the conditions which Franklin had proposed, and De Eomas raised
an electrical kite at Nerac. During a slight storm, this last observer
was able to draw sparks 4 metres (13 feet) in length from the
extremity of a cord, by means of a discharger ; the explosions might
be compared to those of fire-arms.

Lastly, De Saussure discovered by an electroscope surmounted by
a metallic rod, that thunder-clouds are electrified sometimes positively
and sometimes negatively. When two clouds charged with contrary
electricities come together, the violent combination of the two elec-
tricities gives rise to the production of a spark, which is lightning.
If the discharge takes place between a cloud and the earth, the
same luminous phenomenon is seen; but then the thunder is said
to fall, and the lightning is called a thunderbolt.

The form of lightning is sometimes that of a sinuous curve, and
sometimes that of a zigzag rectilinear line ; at other times it does not
take any precise and determined form, and only produces a confused
glimmer illuminating that portion of the sky in which it appears, but
the last appearance is probably owing to the interposition of clouds
which hide the actual flash from the observer. There is also ball
lightning, which moves like a globe of fire through the atmosphere,
with much less velocity than that of other kinds of lightning. It
often happens that the electric flash of thunder-clouds is divided
into 'several branches, forming what is called forked lightning.

The colour of the light of lightning is usually white, sometimes
purplish or violet, or greenish.

Sir Charles Wheatstone has measured, by a very ingenious method,
the mean duration of a flash of lightning. He used a wheel having
a great number of flat silver spokes, which was turned with great
rapidity on its axis ; the wheel being suddenly illuminated during its
rotation by a light with an appreciable duration, for instance TVth of
a second : each spoke being displaced during that time will appear

vii.j ATMOSPHERIC METEORS. 667

thickened on account of the persistence of the luminous impressions
on the retina ; the matter of the wheel will appear more or less
continuous. The same thing takes place with a carriage-wheel which
rapidly passes before us. Now, Wheat-stone greatly increased the
rapidity of the rotation, and always, when the lightning illuminated
the wheel, it seemed immoveable, and the spokes remained distinct
to the sight and at rest. He concluded from numerous experiments
that lightning does not last so much as a thousandth part of a
second.

The violence of the discharge which is effected between two
thunder-clouds gives rise to the noise which we know under the
name of thunder. It must be remarked that the explosion is much
sharper and more brilliant the nearer the lightning is to the observer,
but in almost every case the detonation is accompanied by a pro-
longed roll. The cause of this persistence of the noise of the
discharge is due probably to two causes: first, it has been proved
that a flash of lightning is often many miles in length, and one
of the two extremities may be nearer the person who listens than
the other ; and although the sound is produced at the same instant
in the whole length of the flash, as it takes one second to travel
1,120 yards, many seconds will be required for a distance of 10
miles. Moreover the sound reflected from the clouds and the ground,
gives rise to echoes more or less prolonged. The zigzag form of
lightning also explains how it is that the roll of thunder does not
die away gradually, and that during its duration it is heard louder
at different times.

The effects of thunderbolts present a perfect analogy with those
produced by electrical discharges in machines and batteries ; only
they are infinitely more intense, as we may well imagine from the
prodigious grandeur of the scale on which Nature works. They have
been seen to overturn and carry to a distance considerable masses,
such as walls and masses of rock ; to melt and volatilize metals, to
pierce holes through sand, which is then found vitrified and forms a
kind of tube known as a fulgurite. This last singular phenomenon
has been produced by the help of the great battery of the Conser-
vatoire des Arts et Metiers, and tubes have been obtained similar
to fulgurites by passing a discharge through a bed formed of sand
mixed with salt.

668 PHYSICAL PHENOMENA. [BOOK

We have said above that lightning sometimes reverses the poles
of the magnetic needles in compasses, or completely demagnetizes
them : at other times, it produces a contrary phenomenon and
magnetizes pieces of steel which it strikes.

Its physiological effects are not less curious ; unfortunately they
are sometimes terrible. Men and animals struck with lightning are
often killed on the spot. There are one or two examples in which
the shock produced by it has cured persons afflicted with paralysis
and rheumatism.

Thunder-clouds, when they pass over objects situated on the
ground, electrify them by induction. Such is the cause of the
luminous tufts which are sometimes seen at the summits of pointed
edifices, masts and ships' yards. These faint lights the ancients
regarded as warnings, and sailors now call them Saint Elmo's fires ;
they are explained by the considerable electric tension which con-
ductors have when terminated in a point.

In describing the lightning-conductor in the "Applications of
Physics " which will follow this volume, we give details of the course
followed by lightning and the means of preservation from its terrible
influence.

We have already mentioned the magnificent phenomenon known
as the polar aurora, which is seen in all its beauty in the northern
and southern regions of our globe. It is now no longer a matter
of doubt that there exists a relationship between this luminous
phenomenon and terrestrial magnetism ; that is, between the pro-
duction of the aurora borealis and the variations of the electric
currents which intersect the earth. Arago established, by exact
observations, the coincidence of certain perturbations of the magnetic
needle with the appearance of auroras. These agitations commence
many hours before the appearance of the light, and they are more
and more intense during its continuance. A magnificent experiment
of M. de la Rive has placed beyond doubt the electrical or magnetic
nature of the aurora.

The auroras boreales are visible in our climate, but they are rare
and of short duration. "In the north," says M. Charles Martins,
" the phenomenon is seen with such a brilliancy and magnificence
that nothing can be compared to it. Bright and varied like fire-

vn.] ATMOSPHERIC METEORS. 669

works, this spectacle changes every instant. The painter has not
time to seize the forms and tints of these fugitive lights ; the poet
must give up describing them. Never does one aurora borealis
resemble another ; they vary infinitely." (Du Spitzberg au Sahara.)

The aurora borealis reproduced in our frontispiece from the
beautiful plates in the Voyage au Spitzberg et en Laponie, the obser-
vation and description of which are due to M. Lottin, will give some
idea of the magnificence of the phenomenon. The following is also
a description which we have borrowed from M. Charles Martins,
one of the savants who, with M. Bravais, Lottin, &c., composed the
scientific commission of the expedition : —

" Sometimes the aurorse are simple diffused lights or lumi-
nous sheets; sometimes agitated rays of a brilliant white, which
pass over the whole firmament, starting from the horizon as if
an invisible pencil passed over the celestial vault; sometimes it
is at rest; the unfinished rays do not reach the zenith, but the
aurora is continued at another point ; a cluster of rays starts out,
spreading fan-like, then gets fainter and disappears. At other
times long golden draperies float over the head of the spectator,
folding over each other in a thousand ways, and undulate as if
the wind agitated them, In appearance they are slightly raised in
the atmosphere, and one was astonished not to hear the crackling
of the sheets which glided one over the other. Generally, a lumi-
nous arc is spread towards the north ; one blaok segment separates
it from the horizon, and contrasts by its deep colour with the arc
of brilliant white or red which darts out its rays, is extended,
divided, and soon represents a luminous fan which fills the northern
sky and rises gradually towards the aenith, where its rays, uniting,
form a crown which, in its turn, darts luminous jets in every
direction. Then the sky appears a cupola of fire ; blue, green,
yellow, red, and white, join in the palpitating streamers of the
aurora. But this brilliant spectacle only lasts a few seconds. The
crown first ceases to send out its luminous jets, then by degrees
fades away : a diffused light fills the sky ; here and there some lumi-
nous patches, similar to light clouds, spread themselves and contract
with wonderful activity, like a palpitating heart. Soon they fade
in their turn : all is confused and effaced ; the aurora seems to be
in its agony : the stars, which its light obscured,, shine with a fresh

670 PHYSICAL PHENOMENA. [BOOK vir.

brightness, and the long polar night, dark and profound, again reigns
alone among the snowy solitudes of earth and ocean."

Bravais — in discussing the forms of a great number of arcs,
chosen from among the more regular ones, which had been observed
simultaneously by two observers, and taking one seen at Bossekop
and at Jupvig, distant from the first station about 10 miles — showed
that they could be considered as circular rings in perspective, having
their centre on the radius of the earth directed towards the magnetic
pole, and their plane perpendicular to this radius. He moreover con-
cluded that the height of the rings above the surface of the earth is
comprised between 60 and 120 miles, so that these phenomena occur
in the regions near the extreme limits of the atmosphere.

The brilliancy of the brightest aurora is considerable. Bravais
was able to read by its light a page of small print almost as easily
as by the light of the full moon. Auroras are then, to the sparse
inhabitants of the icy regions near the poles, beneficent phenomena,
and a distraction during the long nights lasting half a year; they
contribute with the brightness of the moou and the twilight to
lessen the sadness and monotony of Nature as she shows herself in
those inhospitable regions.

APPENDIX.

APPENDIX,

DISCOVERY OF OXYGEN IN THE SUN BY PHOTOGRAPHY, AND
A NEW THEORY OF THE SOLAR SPECTRUM.*

I PROPOSE in this preliminary paper to indicate the means by
which I have discovered oxygen, and probably nitrogen, in the
sun, and also to present a new view of the constitution of the
solar spectrum.

Oxygen discloses itself ly bright lines or lands in the solar spectrum
and does not give dark absorption lines like the metals. We must
therefore change our theory of the solar spectrum, and no longer
regard it merely as a continuous spectrum with certain rays absorbed
by a layer of ignited metallic vapours, but as having also bright lines
and bands superposed on the background of continuous spectrum.
Such a conception not only opens the way to the discovery of others
cf the non-metals, sulphur, phosphorus, selenium, chlorine, bromine,
iodine, fluorine, carbon, &c., but also may account for some of
the so-called dark lines, by regarding them as intervals between
bright lines.

It must be distinctly understood that in speaking of the solar
spectrum here, I do not mean the spectrum of any limited area upon
the disc or margin of the sun, but the spectrum of light from the
whole disc. I have not used an image of the sun upon the slit of
the spectroscope, but have employed the beam reflected from the
flat mirror of the heliostat without any condenser.

In support of the above assertions the accompanying photograph

1 Paper by Prof. Henry Draper, M.D. Read before the American Philoso-
phical Society, July 20, 1877. We are indebted to Dr. Draper's kindness for
the plate and illustrations which accompany this paper.

3 F

G74 APPENDIX.

of the solar spectrum with a comparison spectrum of air, and also
with some of the lines of iron and aluminium, is introduced. The
photograph itself is absolutely free from handwork or retouching.
It is difficult to bring out in a single photograph the best points of
these various substances, and I have therefore selected from the
collection of original negatives that one which shows the oxygen
coincidences most plainly. There are so many variables among the
conditions which conspire for the production of a spectrum that
many photographs must be taken to exhaust the best combinations.
The pressure of the gas, the strength of the original current, the
number of Leyden jars, the separation and nature of the terminals, the
number of sparks per minute, and the duration of the interruption in
each spark, are examples of these variables.

In the photograph the upper spectrum is that of the sun, and
above it are the wave-lengths of some of the lines to serve as
reference numbers. The wave4engths used in this paper have been
taken partly from Angstrom, and partly from my photograph of the
diffraction- spectrum published in 1872. The lower spectrum is that
of the open-air Leyden spark, the terminals being, one of iron and the
other of aluminium. I have photographed oxygen, nitrogen, hydrogen,
and carbonic acid, as well as other gases in Plltcker's tubes, and
also in an apparatus in which the pressure could be varied, but for
the present illustration the open-air spark was, all things considered,
best. By other arrangements the nitrogen lines can readily be made
as sharp as the oxygen are here, and the iron lines may be increased
in number and distinctness. For the metals the electric arc gives
the best photographic results, as Lockyer has so well shown ; but
as my object was only to prove by the iron lines that the spectra
had not shifted laterally past one another, those that are here shown
at 4325, 4307, 4271, 4063, 4045, suffice. In the original collodion
negative many more can be seen. Below the lower spectrum are
the symbols for oxygen, nitrogen, iron, and aluminium.

No close observation is needed to demonstrate to even the most
casual observer that the oxygen lines are found in the sun as bright
lines, while the iron lines have dark representatives. The bright
iron line at G (4307), on account of the intentional overlapping of
the two spectra, can be seen passing up into the dark absorption
line in the sun. At the same time the quadruple oxygen line

APPENDIX. 675

between 4345 and 4350 coincides exactly with the bright group in
the solar spectrum above. This oxygen group alone is almost
sufficient to prove the presence of oxygen in the sun, for not only
does each of the four components have a representative in the
solar spectrum, but the relative strength and the general aspect of
the lines in each case is similar. I do not think that in com-
parisons of the spectra of the elements and sun enough stress has
been laid on the general appearance of lines apart from their mere
position ; in photographic representations this point is very pro-
minent. The fine double line at 4319, 4317, is plainly represented
in the sun. Again, there is a remarkable coincidence in the double
line at 4190, 4184. The line at 4133 is very distinctly marked.
The strongest oxygen line is the triple one at 4076, 4072, 4069 ;
and here again a fine coincidence is seen, though the air spectrum
seems proportionately stronger than the solar. But it must be
remembered that the solar spectrum has suffered from the trans-
mission through our atmosphere, and this effect is plainest in the
absorption at the ultra-violet and violet regions of the spectrum.
From some experiments I made in the summer of 1873, it appeared
that this local absorption is so great, when a maximum thickness of'
air intervenes, that the exposure necessary to obtain 'the ultra-violet
spectrum at sunset was two hundred times as long as at mid-day.
I was at that time seeking for atmospheric lines above H like those
at the red end of the spectrum, but it turned out that the absorptive
action at the more refrangible end is a progressive enfeebling, as if
a wedge of neutral-tinted glass were being drawn lengthwise along
the spectrum towards the less refrangible end.

I shall not attempt at this time to give a complete list of the
oxygen lines with their wave-lengths accurately determined, and it
will be noticed that some lines in the air spectrum which have bright
analogues in the sun are not marked with the symbol of oxygen.
This is because there has not yet been an opportunity to make the
necessary detailed comparisons. In order to be certain that a line
belongs to oxygen, I have compared, under various pressures, the
spectra of air, oxygen, nitrogen, carbonic acid, carburetted hydrogen,
and cyanogen. Where these gases were in Pliicker's tubes a double
series of photographs has been needed, one set taken with and the
other without Leyden jars.

3 F 2

676 APPENDIX.

As to the spectrum of nitrogen, and the existence of this element
in the sun, there is not yet certainty. Nevertheless, even by com-
paring the diffused nitrogen lines of this particular photograph, in
which nitrogen has been sacrificed to get the best effect for oxygen,
the character of the evidence appears. The triple band between 4240,
4227, if traced upward into the sun, has approximate representatives.
Again, at 4041 the same thing is seen, the solar bright line being
especially marked. In another photograph the heavy line at 3995,
which in this picture is opposite an insufficiently exposed part of the
solar spectrum, shows a comparison band in the sun.

The reason I did not use air in an exhausted Pliicker's tube for
the production of a photograph to illustrate this paper, and thus get
both oxygen and nitrogen lines well defined at the same time, was
partly because a brighter light can be obtained with the open-air
spark on account of the stronger current that can be used. This
permits the slit to be more closed, and of course gives a sharper
picture. Besides, the open-air spark enabled me to employ an iron
terminal, and thus avoid any error arising from accidental displace-
ment of the reference spectrum. In Pliicker's tubes with a Leyden
spark the nitrogen lines are as plain as those of oxygen here. As
far as I have seen, oxygen does not exhibit the change in the
character of its lines that is so remarkable in hydrogen under the
influence of pressure as shown by Frankland and Lockyer.

The bright lines of oxygen in the spectrum of the solar disc
have not been hitherto perceived, probably from the fact that in eye
observation bright lines on a less bright background do not make
the impression on the mind that dark lines do. When attention
is called to their presence they are readily enough seen, even without
the aid of a reference spectrum. The photograph, however, brings
them into a greater prominence. From purely theoretical considera-
tions derived from terrestrial chemistry and the nebular hypothesis,
the presence of oxygen in the sun might have been strongly
suspected, for this element is currently stated to form eight-ninths
of the water of the globe, one-third of the crust of the earth, and
one-fifth of the air, and should therefore probably be a large con-
stituent of every member of the solar system. On the other hand,
the discovery of oxygen, and probably other non-metals, in the sun,
gives increased strength to the nebular hypothesis, because to many

APPENDIX. 677

persons the absence of this important group has presented a con-
siderable difficulty.

At first sight it seems rather difficult to believe that an ignited
gas in the solar envelope should not be indicated by dark lines in
the solar spectrum, and should appear not to act under the law
that " a gas when ignited absorbs rays of the same refrangibility as
those it emits." But in fact the substances hitherto investigated in
the sun are really metallic vapours, hydrogen probably coming under
that rule. The non-metals obviously may behave differently. It is
easy to speculate on the causes of such behaviour, and it may be
suggested that the reason of the non-appearance of a dark line may
be that the intensity of the light from a great thickness of ignited
oxygen overpowers the effect of the photosphere, just as if a person
were to look at a candle flame through a yard thickness of ignited
sodium vapour, he would only see bright sodium lines, and no dark
absorption lines. Of course, such an explanation would necessitate
the hypothesis that ignited gases such as oxygen give forth a
relatively large proportion of the solar light. In the outburst of
T. Coronce Huggins showed that hydrogen could give bright lines
on a background of spectrum analogous to that of the sun.

However all that may be, I have no doubt of the existence of
substances other than oxygen in the sun which are only indicated
by bright lines. Attention may be called . to the bright bands near
G, from wave-lengths 4307 to 4337, which are only partly accounted
for by oxygen. Farther investigation in the direction I have thus
far pursued will lead to the discovery of other elements in the sun,
but it is not proper to conceal the principle on which such researches
are to be conducted for the sake of personal advantage. It is also
probable that this research may furnish the key to the enigma of
the D3 or Helium line, and the 1474 K or Corona line. The case of
the D3 line strengthens the argument in favour of the apparent
exemption of certain substances from the common law of the relation
of emission and absorption, for while there can be no doubt of the
existence of an ignited gas in the chromosphere giving this line,
there is no corresponding dark line in the spectrum of the solar
disc.

In thus extending the number of elements found in the sun we
also increase the field of inquiry as to the phenomena of dissociation

678 APPENDIX.

and recomposition. Oxygen, especially from its relation to the
metals, may readily form compounds in the upper regions of the
solar atmosphere which can give banded or channelled spectra. This
subject requires careful investigation. The diffused and reflected
light of the outer corona could be caused by such bodies cooled
below the self-luminous point.

This research has proved to be more tedious and difficult than
would be supposed,, because so many conditions must conspire to
produce a good photograph. There must be a uniform prime moving
engine of two-horse power, a dynamo-electric machine thoroughly
adjusted, a large Kuhmkorff coil with its Foucault break in the best
order, a battery of Leyden jars carefully proportioned to the Pliicker's
tube in use, a heliostat, which of course involves clear sunshine, an
optical train of slit, prisms, lenses, and camera well focussed, and in
addition to all this a photographic laboratory in such complete con-
dition that wet sensitive-plates can be prepared which will bear an
exposure of fifteen minutes and a prolonged development. It has
been difficult to keep the Pliicker's tubes in order; often before the
first exposure of a tube was over the tube was ruined by the strong
Leyden sparks. Moreover, to procure tubes of known contents is
troublesome. For example, my hydrogen tubes gave a spectrum
photograph of fifteen lines of which only three belonged to hydrogen.
In order to be sure that none of these were new hydrogen lines it
was necessary to try tubes of various makers, to prepare pure
hydrogen and employ that, to examine the spectrum of water, and
finally to resort to comparison with the sun.

The object in view in 1873, at the commencement of this research,
was to secure the means of interpreting the photographs of the
spectra of stars and other heavenly bodies obtained with my 28-inch
reflector. It soon appeared that the spectra of nitrogen and other
gases in Pliicker's tubes could be photographed, and at first some
pictures of hydrogen, carbonic acid, and nitrogen were made, because
these gases seemed to be of greatest astronomical importance on
account of their relation to stars, nebulae, and comets. Before the
subject of comparison spectra of the sun was carefully examined
there was some confusion in the results, but by using hydrogen the
source of these errors was found out.

But in attempting to make a prolonged research in this direction,

APPENDIX. G79

it soon appeared that it was essential to be able to control the
electrical current with precision, both as to quantity and intensity,
and moreover to have currents which, when once adjusted, would
remain constant for hours together. These conditions are almost
impossible to attain with any form of battery, but on the contrary
are readily satisfied by dynamo-electric machines. Accordingly, I
sought for a suitable dynamo-electric machine and motor to drive it,
and after many delays procured a combination which is entirely
satisfactory. I must here acknowledge my obligations for the suc-
cessful issue of this search to Prof. George F. Barker, who was the
first person in America to procure a Gramme machine. He was also
the first to use a Brayton engine to drive a Gramme.

FIG. 455. — The Gramme machine.

The dynamo-electric machine selected is one of Gramme s patent,
made in Paris, and is a double-light machine, that is, it has two
sets of brushes, and" is wound with wire of such a size as to give
a current of sufficient intensity for my purposes. It is nominally
a 350-candle-light machine, but the current varies in proportion
to the rate of rotation, and I have also modified it by changing
the interior connections. The machine can produce as a maximum
a light equal to 500 standard candles, or by slowing the rotation
of the bobbin, the current may be made as feeble as that of tho

680

APPENDIX.

weakest battery. In practical use it is sometimes doing the work
of more than fifty large Grove nitric acid cells, and sometimes the
work of a single Smee.

The Gramme machine could not be used to work an induction
coil when it vfirst reached me, because when the whole current was
sent through the Foucault interrupter of the Euhmkorff coil,
making 1,000 breaks per minute, the electro-magnets of the
Gramme did not become sufficiently magnetized to give an ap-
preciable current. But by dividing the current so that one pair
of the metallic brushes, which collect from the revolving bobbin,
supplied the electro-magnets, the other pair could be used for
exterior work, no manner whether interrupted or constant. The

Fio. 40t5. — Bray toil's petroleum motor.

current obtained in this way from one pair of brushes when the
Gramme bobbin is making 1,200 revolutions per minute is equal
to 100 candles, and is greater in quantity and intensity than one
would like to send through a valuable induction coil. I usually
run the bobbin at 622 revolutions per minute, and this rate will
readily give 1,000 10-inch sparks per minute with the 18-inch coil.
Of course a Pliicker's tube lights up very vividly and generally ; in
order to get the maximum effect I arrange the current so that the
aluminium terminals are on the point of melting. The glass,
particularly in the capillary part, often gets so hot as to char
paper. The general appearance of the machine is shown in Fig. 455.

APPENDIX. 681

As long as the Gramme bobbin is driven at a steady rate the
current seems to be perfectly constant, but variations of speed make
marked differences in the current, and this is especially to be avoided
when one is so near the limit of endurance of Pliicker's tubes. A
reliable and constant motor is therefore of prime importance for
these purposes. A difference of one per cent, in the speed in the
engine sometimes cannot be tolerated, and yet at another time one
must have the power of increasing and diminishing the rate through
wide limits. The only motor, among many I have examined and
tried, that is perfectly satisfactory, is Brayton's Petroleum Ready
Motor.

This remarkable and admirable engine acts like an instrument
of precision. It can be started with a match, and comes to its
regular speed in less than a minute ; it preserves its rate entirely
unchanged for hours together. Moreover, it is economical, cleanly,
and not more noisy than a steam-engine. The one of two-horse
power I have, ran for six months, day and night, supplying water
and air to the aquaria in £he Centennial Exhibition at Philadelphia.
At any time on going into the laboratory it can be started in a lew
seconds, even though it has not been running for days.

3 G

INDEX.

3 G 2

INDEX.

J^pinus, his method of magnetization, 524;

his electrical condenser, 570.
Aerolites, 15.

Air, its weight and other qualities, 84.
Air-condensing machines, 115.
Air-pump, 85, 107, 129.
Alcohol, vaporization of, 449.
Alcohol thermometers, 427.
Aldini's electrical experiments, 603
Amber, its electrical property known to

the ancients, 531, 532, 535.
Amianthus, its incombustibility, 482.
Ampere, his researches in electro-magnet-
ism, 605, 611, 613, 619.
Analysis of light, 309 (see Spectrum

Analysis).

Aneroid barometers, 100.
Angstrom, his map of lines in the solar

spectrum, 325, 333, 355.
Aqueous meteors (see Atmospheric Me-
teors).

Arabs, their early use of the compass, 519.
Arago, his researches : velocity of sound,
133 ; photometry, 245 ; undulatory
theory of light, 363 ; chromatic polari-
zation of light, 392, 405 ; electro-
magnetism, 615.

Archimedes' principle of the loss of weight
of immersed bodies, 74 ; its application
to gases, 115.

Arcturus, heat radiated by, 496
Areometer, or Hydrometer, 80.
Armstrong's hydro-electrical machine, 559.
Asbestos, its incombustibility, 482.
Atmosphere, 84.
Atmospheric currents, their effect on the

barometer, 665.
ATMOSPHERIC METEORS, Book VII., 643 —

670.

Attraction, laws of, 13, 16.
Attraction and repulsion : magnetic, 612 ;

electrical, 531.
Attwood's machine, 24, 25.
Aurora borealis, 220 ; its electric or mag-
netic nature, 521, 668 ; described, as
seen at Spitzbergen, 669.
Avalanches, 7.

Babinet, M., on the interference of lumi-
nous rays, 364, 365.

Balance, 52.

Barometer, 89-101.

Barometric pressure, variations of, 664.

Baroscope, 115.

Bartholin, Dr. Erasmus, his discovery of
double refraction of light, 376.

Beams, pencils, and rays of light, 225.

Becquerel, Edmond, his researches on
phosphorescence, 344 ; his phosphoro-
scope, 345.

Bianchi's air-pump, 111-113.

Biot, his researches; on phosphorescence,
343 ; properties of tourmaline, 391 ;
polarization of light by simple refrac-
tion, 392 : chromatic polarization, 399,
405.

Bi-refractive substances (see Double Re-
fraction of Light).

Bismuth, its low power as a heat conductor,
479, 480 ; specific heat, 487.

Bologna, Leaning Tower of, 50.

Bologna phosphorus, 342.

Borda's pendulum, 41.

Bouguer's photometer, 244.

Bourdon's aneroid barometer, 100.

Boyle's improvements of the air-pump,
107.

Brandt's discovery of phosphorescence, 341 :

Breguet's metallic thermometer, 430.

Brewster's investigations and discoveries ;
the solar spectrum, 326 ; interference
of luminous rays, 365 ; polarization of
light by simple refraction, 392 ; chro-
matic polarization, 399, 402.

Bristol Cathedral, effects of heat and cold
on leaden roof, 433.

Brunner on expansion of ice by heat, 439.

Buffon's experiments with burning mirrors,
462, 464.

Bunsen's discoveries in spectrum analysis,
328-330; his electric battery, 597.

Bunten's improvements in barometers, 96,
98.

Burning glasses and burning mirrors, 462,
463.

686

INDEX.

Caesium discovered by spectrum analysis,

329.

Cagniard-Latour's Syren, 153.
Calcium sulphides, their phosphorescence,

344.

"Calorie," or unit of heat, 485.
Calorimetry, measurement of the specific

heat of 'bodies, 484-491.
Camera obscura, 228, 230, 301.
Canton's phosphorus, 342.
Capacity, French and English units of,

Introd. Cfiap., xxxv.
Cathetometer, 95.
Cat's-skin, electricity produced by, 536,

537, 561.

Centrigrade thermometer, 424.
Centre of gravity, 45.
Centre of pressure on immersed bodies, 73.
Charles' areometer, 80.
Chemical balance, 52.
Chemical harmonicon, 128.
Chemical effects of electricity, 583.
Chevalier, M. C., his modification of the

camera obscura, 302.
Chevreul, M, , his work ' ' Des Couleurs et

de leurs Applications aux Arts Indus-

triels," 321, 336.

Chinese, their early use of the compass, 519.
Chladni's illustrations of the vibrations of

a plate, 176.

Clang-tint of the voice and musical instru-
ments, 151, 204, 214.
Clarke's magneto-electric machine, 625.
Clothing, bad conductors of heat used for,

481, 483.
Clouds, 659.

Cohesion of solids and liquids, 59,
Colour, phenomena of, 218 (see Light).
Coloured rings and colours of thin plates,

Newton's discoveries, 368, 369.
Combustion and flame, 519.
Compass, magnetic, 497, 519.
Compressibility of gases, 118 ; of liquids,

61.

Compression a source of heat, 502.
Concave mirrors, 259.
Condensing machines, 115.
Conduction, heat transmitted by, 477-483;

table of conducting powers of solids,

479 ; conductivity of liquids and gases,

482, 483.

Congelation of water and mercury, 445,

446 ; expansive force of frozen water,

446.

Conical mirrors, 268.
Contraction : by cold, 432 ; of iodide of

silver, by heat, 432 ; of water between

0° and 4°, 441.
Convex mirrors, 264.
Cooke's aneroid barometer, 101.
Coulomb's magnetic balance, 522 ; electric

balance, 541.
Cruikshank's electric trough pile, 593.

Crystals, conductivity of heat in, 480.
Ctesibius, invention of pumps ascribed to

him, 102.
Cuneus, his discovery of the Levden iar,

567, 568.
Cupping, an illustration of atmospheric

pressure, 91.

Currents, 8 (and see Atmospheric Currents).
Cylindrical mirrors, 267.

Dalibard's electrical experiments : light-
ning. 666.

Dalton's formation of vapours in vacua,
452.

Daniell's electric battery, 596.

Davy, Sir H., his researches : reflection of
radiant heat, 461 ; safety lamp, 481;
melting ice by friction, 501 ; electrical
experiments, 598-600 ; the voltaic arc,
638.

De Dominis, Antonio, theory of the rain-
bow, 650.

Deleuil's air-pump, 112.

Delisle's thermometer, 424.

Density : of the earth, 44 ; of solid bodies,
57, 79, 80 ; of liquids, 70, 76.

De Romas' electrical experiments : light-
ning, 666.

Desaguliers' experiment on falling bodies,
33.

De Saussure's hair hygrometer, 655 ; his
experiments, 665.

Descartes' discovery of the laws of refrac-
tion of light, 277 ; his laAv of double
refraction of light, 379, 383 ; his theory
of the rainbow, 650.

Despretz, his experiments : expansion and
contraction of water, 441 ; conductivity
of liquids, 483 ; combustion, 499 ;
electricity, 600.

Dew, 659.

Dew-drops, spherical form of, 60.

Dial barometer, 99.

Diffraction of light, 357-366.

Dilatation by heat of solids, liquids, and
gases, 416-420; thermometers, 421-
432.

Double refraction of light, 376-384.

Draper on the discovery of oxygen and
nitrogen in the sun, Appendix.

Drebbel, Cornelius, his air thermometer.

427.

Drummond's light, 638.
Duhamel's method of magnetization, 524.
Dutch tears, or Rupert's drops, 435.

Ear, the (see Hearing and the Voice).

Ear of Dionysius, 159.

Earth, the : its form and constitution, 5 ;
oblateness, 40 ; density, 44 ; heat of
its interior, 496 ; terrestrial magnetism,

INDEX.

687

521, 525, 624 ; connection between
aurora and terrestrial magnetism, 668.

Earthquakes, 6, 124, 131, 161.

Echoes, 139, 140.

Eclipses of Jupiter's satellites, 233.

ELECTRICITY, Book VI., 529—642.

Electricity a source of light, 220.

Electric telegraph, 618.

Electro-magnetism, 604-619.

Equilibrium, phenomena and laws of, 1.
119; of heavy bodies, 45 ; of liquids,
70, 72 ; of bodies immersed in liquids,
73.

Ether, 351.

Fahrenheit's areometer, 82.

Fahrenheit's thermometer, 424.

Falling bodies, 12, 16, 33.

Faraday's experiments : distribution of
electricity on bodies, 540 ; Leyden jar
with moveable coatings, 572 ; electrical
experiments, 602 ; induction currents,
620.

Fire (see Heat).

Fire-syringe, 88.

Fish, their movements in water, 77.

Fizeau, M., his measurement of the velo-
city of light, 235 ; experiments on the
velocity of light, 356 ; contraction of
iodide of silver by heat, 439 ; electro-
magnetism, 629 ; the voltaic arc, 638.

Florentine Academicians, their experi-
ments on the compressibility of liquids,
61, 103 ; on the weight of air, 88.

Fogs, 659.

Force-pump, 105.

Fortin, his improvements in barometers,
96, 97.

Foucault, Leon, his measurement of the
velocity of light, 235, 237, 353, 356 ;
improvement on Bouguer's photometer,
245 ; discoveries affecting the solar
spectrum, 331 ; researches in electro-
magnetism, 628 ; the voltaic arc, 638.

Fountains, 71, 93.

Frank land and Lockyer, their researches
in spectrum analysis, 329.

Franklin's experiments : on absorption of
heat, 472; causes of thunder and light-
ning, 665.

Fraunhofer's discovery of dark lines in the
solar spectrum, 323-332, 337, 339 ;
laws of diffraction, 358, 364.

Freezing (see Congelation, Ice).

Fresnel's proofs of the undulatory theory
of light, 352, 403 ; diffraction phe-
nomena, 358 ; experiment of the two
mirrors, 360, 361 ; double refraction of
light, 383.

Friction a source of heat, 500.

Friction, electricity produced by, 531,
532.

Fusion of solid bodies, 444.

Galileo's experiments : oh falling bodies,
16 ; inclined plane, 23 ; weight of air,
86 ; motion of the pendulum, 35 ; air
thermometer, 427.

Galvani's electrical experiments, 585, 602.

Galvanometer, its invention by Nobili
609.

Gases : weight, elasticity, compressibility,
and density of, 86; pressure of, 118 ;
their expansion by heat, 441.

Gas microscope, 305.

Gay-Lussac's improvements in barometers,
96, 98 ; expansion of gases, 442 ; in-
strument for measuring heat-conduct-
ing powers, 478; electrical experiments,
602.

Geissler's tubes : stratification of the elec-
tric light, 642.

Geology affected by gravitation, 5.

Ghost produced by reflected light, 271,
273.

Gilbert, William, his discoveries in elec-
tricity, 531.

Glaciers, 7.

Glass : fusion of, 444 ; electrical properties
of, 532, 535, 536 ; perforated by elec-
tricity, 578.

Gold, its heat-conducting power, 479.

Goniometer, 258.

Graphic study of sound vibrations, 155,
197.

Gravesande's improvements of the air-
pump, 107.

GRAVITY, Book I., 1—119.

Grimaldi's experiment : diffraction of light,
357, 361.

Guericke, Otto de, the inventor of the air-
pump, 86, 107 ; of the Magdeburg
hemispheres, 91 ; of the baroscope,
115.

Hail and sleet, 660.

Haldat's instrument for measuring the

pressure of liquids, 66.
Hearing and the Voice, 208-214.
HEAT, Book IV., 415—508.
Heat produced by electricity, 579, 582,

598, 600.
Heat, French and English units of, Introd.

Chap., xxxviii.

Heliography, 338.
Heliostat fo

for constant reflection of solar
rays, 258.

Helmholtz, his resonance globe, 205 ; on
colours of non-luminous bodies, 319.

Herschel, Sir John, on measuring the
intensity of light, 239 ; refraction of
light, 283 ; colours of non-luminous
bodies, 314 ; weight of molecules of
light, 350 ; experiments on diffraction,
362 ; polarization of light, 392.

INDEX.

Hoar-frost, 659.

Huyghens, his undulatory theory of light,
350, 361 ; double refraction of light,
376 ; polarization of light, 386, 392.

Hydraulic press or ram, 62.

Hydraulic tourniquet, 68.

Hydrometers, 80.

Hydrostatic balance, 81.

Hydrostatic phenomena, 62.

Hygrometers : De Saussure's hair hygro-
meter, 655.

Ice ; its expansion by heat, 439, 443, 444 ;
ice-lenses, 464 ; a source of heat to
colder bodies, 492 ; melted by friction,
501 ; electrical properties of, 535, 582 ;
its crystalline texture, ice-flowers, 661.

Icebergs, 7.

Iceland spar, double refraction produced
by, 376-383 ; polarization of light,
386 ; its contraction and expansion,
438 ; absorption of heat, 473 ; conduc-
tivity of heat, 480.

Indium discovered by spectrum analysis,
329.

Induction, phenomena of (see Electricity).

Interference of luminous waves, 358-366.

Iodide of silver, its contraction by heat,
439.

Iridescent colours in thin plates, 367.

Iron : its expansion and contraction by
heat and cold, 434, 438 ; fusing point,
444 ; heat-conducting power, 479 ;
480 ; specific heat, 487 ; as a magnetic
substance, 509-528 ; fusion by electri-
city, 598 ; by electro-magnetism, 630 ;
magnetization of, 614, 626.

Joule, Dr., experiments on the mechanical

equivalent of heat, 505.
Jupiter's satellites, their eclipses a proof

of the velocity of light, 232.

Kaleidoscope, 256.
Kinnersley's thermometer, 566.
Kirchhoff's discoveries : lines in the solar

spectrum, 325, 331 ; new metals dis-

covered by spectrum analysis, 328, 329.
Koenig, M., his optical study of musical

sounds by manometric flames, 199-

203.

Laplace and Lavoisier : their measurement
of linear expansion of solids, 436 ; ice
calorimeter, 490 ; experiments on com-
busion, 499.

Leaning Tower of Pisa, 16, 50 ; of Bologna,
60.

Leichtenberg's distribution of positive and
negative electricities, 574.

Length, French and English units of,
Introd. Chap., xxxv.

Lens of the solar microscope, 304 • of the
spectroscope, 327 ; diverging and con-
verging lenses, their form and foci,
images seen, 291, 300 ; lens-pri-m of
the camera obscura, 301 ; megascope,
302 ; magic lantern phantascope, 303 ;
solar microscope, 304 ; used in discover-
ing the colours of thin plates, 369 ;
burning glasses, Buffon's echelon lens,
463, 464 ; fire procured by lenses of
ice, 464.

Le Konx on the electric light and voltaic
arc, 639.

Leslie, his differential thermometer, 428 ;
his experiments on the emissive powers
of heat in bodies, 466.

Leyden jar, 567

LFGHT, Book III., 215—412.

Light, electric, 631-642.

Lightning, cause and phenomena of: ex-
periments of Franklin, Dalibard, De
Eomas, De Saussure, and Wheatstone,
220, 665-668.

Liquids : weight of, 58 ; cohesion, 59 ;
compressibility, 61 ; pressure, 62 ;
density, 70 ; specific gravity, 82 ;
expansion by heat, 432, 439. (See
Ebullition, Evaporation, Heat, Vapori-
zation )

Lissajous' method for the optical study of
musical sounds, 193-199.

Lockyer and Frankland, their researches
in spectrum analysis, 329.

Magdeburg hemispheres illustrating atmo-
speric pressure, 92.

Magic lantern, 303.

Magic mirror, 257.

MAGNETISM, Book V., 509—528.

Malus, his discovery of polarization of
light by reflection and simple refrac-
tion, 392.

Manometer, 110.

Mariotte's law of the compressibility of
gases, 102-118.

Mass distinguished from weight, 46.

Mass, French and English units of, Introd.
Chap., xxx vii.

Matteucci's researches on phosphorescence,
343.

Meyer, Dr., his theory of the mechanical
equivalent of heat, 505.

Mechanical equivalent of heat, 485, 505.

Mechanical work, French and English
units of, Introd. Chap., xxxviii.

Megascope, 303.

Melloni, his thermo-electric pile, reflecting
powers of heat in bodies, 468 ; measure-
ments of diathermanovis powers, 474.

INDEX.

689

Mercury : cohesion of its particles,
Torricelli's tube ; the barometer, 89 ;
94 ; purity of the liquid, 94 ; its
expansion by heat, 421 ; co-efficients
of cubic expansion by heat, 440 ;
temperature of vaporization, 449 ;
specific heat, 487. (See Barometer,
Thermometers,)

Metals, table of expansion by heat, 438.

Meteorology : dew, clouds, hoar-frost,
fogs, snow, sleet, hail, ice, variations
of barometric pressure, wind, 659-665.
(See Barometer, Thermometers.)

Meteors, 124, 131, 161.

Mirage, Monge's theory of the, 646,

Mirrors, 252-270 : plane, 252 ; parallel
or inclined, multiple reflections, 254 ;
kaleidoscope, 256 ; concave mirrors,
259-264 ; convex, 264 ; cylindrical,
267 ; conical, 268 ; magic mirror, or
polemoscope, 257.

Molecular cohesion, 59.

Monge, his theory of the mirage, 646.

Moon, The, as a source of light, 220.

Morin's machine for exhibiting the laws of
falling bodies, 24, 29.

Motion, phenomena of, 6 ; heat a source of
motion, 504-508.

Mother-of-pearl, iridescent colours of, 365 ;
double refraction of, 384,

Muschenbroeck, his improvements of the
air-pump, 107 ; experiments with the
Leyden jar, 567.

Musical sounds : "pitch/' 151 ; the gamut,
185, 186 ; intervals, 188 ; modula-
tions, 190 ; major scale, sharps and
flats, 190 ; minor scale, 191 ; optical
study of sounds, Lissajous' method,
193-199; Koenig's employment of
manometric flames, 199-203 ; -quality
of musical notes, clang-tint or timbre,
204; Helmholtz's resonance globe, 205;
Koenig's apparatus, 206 ; harmonies in
vowel sounds, 207.

Nairne's electrical machine, 558.

Necker, M. A., interference of luminous
rays, 366.

Newton's researches and experiments : on
gravity, 34 ; colours in light sources,
306, 309, 310, 311, 313 ; emission
theory of light, 349 ; diffraction, 358,
361 ; the soap-bubble and colours of
thin plates, 367 ; coloured rings, 369 ;
the rainbow, 6£0.

Nicholson, invention of the areometer
ascribed to him, 80.

Nicol's prism, polarization of light shown
by, 390.

Nitrogen in the sun, Appendix.

ISobili's galvanometer, 609.

Nollet, Abbe, his electrical experiments,
557, 567.

Oersted's discoveries and experiments in

electro-magnetism, 604-619.
Opacity and transparency, 222.
Optical or luminous meteors, mirage, 646.
Oxy-hydrogen blowpipe, 499.
Oxygen in the sun, Appendix.

Papin's improvements of the air-pump,
107 ; his digester, for raising the
temperature of ebullition, 450.

Pascal's law of equal pressures, 62 ; his
experiment, the hydrostatic paradox,
69 ; experiments on the pressure of the
atmosphere, 89, 90.

Pencils, rays, and beams of light, 225.

Pendulum researches of Galileo and
Huyghens, 35 ; law of its motion,
35.

Penumbra, 226.

Percussion a source of heat, 502.

Perier's experiments with the barometer,
90.

Phantascope, 303.

Phonautography, or graphic study of sono-
rous vibrations, 155.

Phosphorescence discovered by Brandt,
341 ; the glow-worm, flowers, animal-
culse, &c,, 342 ; Becquerel's phosphoro-
scope, 345.

Phosphorescence produced by electric
light, 642.

Phosphorus, electrical properties of,
535.

Photo- electrical microscope, 305.

Photometers : Rumford's, 243 ; Bouguer's,
244.

Pisa, Leaning Tower at, 16, 50.

"Pitch" of sound, 151.

Planets, as sources ot light, 219, 242.

Plumb-line, 22,

Pneumatic-syringe, 88.

Poisson on the uudulatory theory of light,
363.

Polarization of light, 385-405.

Polemoscope, or magic mirror, 257.

Pouillet, M., his pyrheliometer, 493,
496 ; researches in electro-magnetism,
618.

Pressure : of the air upon the earth, 86,
91 ; of liquids, 62, 64 ; on bodies
immersed in liquids, 73.

Principle of Archimedes on the pressure of
immersed bodies, 74 ; its application
to gases, 115.

Prism, the : its geometrical form, devia-
tion of luminous rays, 288-291 ; lens-
prism of the camera obscura, 301 ;
decomposition of solar light, 307 ; its
recomposition, 310.

Prisms employed by Fraunhofer in his
discoveries, 324.

690

INDEX.

Prisms of Iceland spar, their effect in
double refraction and polarization of
light, 376, 386.

Prisms, Nicol's prism, 390.

Ptolemy's observation of atmospheric re-
fraction, 277.

Pumps, 102 119.

Pyrheliometer of M. Pouillet, 493.

Pyrometers, 430, 439.

Quartz, its unequal conductivity of heat,
480.

Railway accidents caused by heat, 434.

Rain, 8, 20.

Rainbow, 308, 650.

Ramsden's plate-glass electrical machine,
557.

Rays, pencils, and beams of light, 225.

Reaumur's thermometer, 424.

Reflection of Light and Sound (see Light,
Sound).

Refraction of Light and Sound (see Light,
Sound).

Refrangibility of coloured rays, 307.

Regnault's air-condensing pump, 117 ;
compressibility of gases, 119; cubic
expansion of mercury, 440 ; specific
heats of bodies, 487, 491 ; mechanical
equivalent of heat, 505.

Resin, its electrical properties, 532, 535,
536, 552, 561.

Robertson's phantascope, 303.

Rochon, Abbe, experiments on solar rays,
luminous and calorific, 337.

Rock-crystal, double refraction of, 383.

Rock-salt, a non-absorbent of heat, 473.

Roemer's discovery of the velocity of light,
234.

Rubidium discovered by spectrum analysis,
329.

Ruhmkorff's induction coil and commuta-
tor, b27, 629.

Rumford's photometer, 243 ; his differen-
tial thermometer, 428 ; experiments on
combustion, 499 ; on heat produced by
friction, 500.

Rupert's drops, or Dutch tears, 435.

Rutherford's photographs of the solar spec-
trum, 338 ; maximum and minimum
thermometers, 662.

Safety -lamps, 481.

St. Elmo's fires, electric lights so called,

604, 668.
Savart's toothed wheel, 152 ; illustrations

of the vibrations of a plate, 175.

Scales (see Balance).

Scattered light, 316.

Schweigger's multiplier, 608 (see Elec-
tricity).

Scientific units, French and English,
Jnlrod. Chap., xxxv.

Seebeck's Syren, 154 ; researches on solar
rays, 337 ; chromatic polarization of
light, 399.

Sextant, 258.

Shadows, 226.

Ships, equilibrium of, 76, 78.

Silbermann's condensing pump, 116.

Silhouettes, 227.

Silver : its power of conducting heat, 479 ;
specific heat, 487 ; fusion by electricity,
598.

Siphon, 106.

Sirius, velocity of its movement, 355.

Sleet and hail, 660.

Snell, Willebrod, his discovery of the laws
of refraction of light, 277.

Snow and snow crystals, 660.

Soap-bubble, Newton's study of the, 367,
372.

Sodium, its spectrum, 328, 329.

Solar microscope, 302.

Solar prominences in eclipses, 334.

Solar spectrum, 307 ; discovery by Wol las-
ton and Fraunhofer of dark lines, 323.

Solar winds, their velocity, 356.

Solenoid, or electrical magnet constructed
by Ampere, 612.

Sonometer, 164.

SOUND, Book II., 121—214.

Sources of heat, 492-503.

Specific gravity, 57 ; of bodies, methods
of determining, 78 ; of liquids, 82 ;
table of, 83.

Spectra of stars, 326 ; of metallic vapours
and gases, 327.

Spectroscope, 327.

Spectrum, Solar (see Solar Spectrum).

Spectrum analysis, 326-335.

Stars, as sources of light, 219 ; as heat
radiators, 496.

Stokes, Professor, his discovery of metallic
vapours in the sun's atmosphere, 331 ;
chemical solar rays, 339.

Suction pump, 103, 105.

Sun, The, as a source of light, 219, 242 ;
its appearance and constitution, inten-
sity of solar heat, 493 ; total heat
radiated, 295.

Surface, French and English units of,
Introd. Chap., xxxvi.

Swimming-bladder of fish, 77.

Syrens for measuring vibrations of sound,
153.

Temperature of space, 496.
Temperature, its effect on magnets, 526 ;
on electricity, 543.

INDEX.

691

Terrestrial magnetism, 521, 525.

Thalen's researches in spectrum analysis,
835.

Thallium discovered by spectrum analysis,
329.

Thermo-electric pile for study of pheno-
mena of heat, 469 ; its use in measuring
heat-radiation of stars, 496.

Thermometers : expansion of gases by
heat, 419 ; temperatures of melting ice
and boiling water, 421 ; determination
of zero and 100°, 422, 423 ; thermo-
metrical scales, Centigrade, Fahrenheit,
Reaumur, and Delisle, 425; Walferdin's
metastatic thermometer, 426 ; alcohol,
ether, and gas as thermometers, Galileo
and Cornelius Drebbel, 427; Leslie
and Rumford's differential thermo-
meters, 428 ; metallic dial thermo-
meter, Breguet's metallic thermometer,
pyrometers, 430 ; Kinnersley's electri-
cal thermometer, 566 ; maximum and
minimum thermometers, 662.

Thermometric degrees, French and English,
Introd. Chap., xxxviii.

Thunder : effects of thunderbolts, 667.

Tides, 15.

Time, measures of (see Pendulum).

Torricelli, his discovery of the principle of
the barometer, 89.

Tourmaline, double refraction of, 383 ;
polarization of light by, 391 ; effects of
tourmaline pincette, 400.

Translucent and transparent substances.
222.

Tyndall, Professor, on calorific solar rays,
340 ; expansive force of freezing water,
446 ; experiments on heat, 473, 475 ;
influence of the ocean on climate, 488 ;
amount of heat radiated by the sun,
495 ; crystalline texture of ice, ice-
flowers, 661.

Umbra and penumbra, 226.
Undulatory theory of light, 372, 404.
Unit of heat, or " calorie," 485.
Units : French and English Scientific,

Units, Introd. Chap., xxxv.
Universal gravitation, 11.

Vacuum, 85, 89, 90, 103, 107 (see Air
Pump).

Van Marum's electrical machine and ex-
periments, 559, 580.

Velocity, French and English units of,
Introd: Chap., xxxviii.

Velocity of light, 231-237, 353 ; of solar
winds, 356 ; of falling bodies, 32 ; of
sound, 132-137 ; of stars measured by
the spectroscope, 333, 335.

Vibrations of Sound (see Sound).

Vidi's aneroid barometer, 101.

Voice, human, 124.

Volcanoes, 8.

Volta, his experiment of electrical hail,
562 ; his electrical discoveries, 583,
585, 593, 597.

Von Guericke, Otto, his electrical machine,
552.

Walferdin's metastatic thermometer, 426 ;
maximum and minimum thermometers,
663.

"Water : salt and fresh, 70 ; expansion and
contraction at different temperatures,
441 ; evaporation, ebullition, and vapo-
rization, 444-452 ; electrical properties
of, 534 ; its decomposition by the
electric pile, 601 (see Force Pump,
Pumps, Siphon, Suction Pump).

Weight of bodies, 1, 45 ; of liquids, 58 ;
of the air and gases, 84 ; of bodies in
vacuo, 115.

Weight, French and English units of,
Introd. Chap., xxxvii.

Wheatstone's experiments : meteors, 665.

Wheel barometer, 99.

Wind, its effect on the barometer, 665.

Wollastou's experiments : in photometry,
245 ; discovery of dark lines in the
solar spectrum, 323 ; researches in chro-
matic polarization of light, 402 ; elec-
tric pile, 594.

Young's principle of interference of lumi-
nous waves, 358, 361.

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